2330:
1091:
817:
1892:
1796:
1516:
1492:
1053:
1015:
901:
1904:
1868:
1856:
1698:
1686:
1504:
703:
660:
1784:
1626:
1614:
2507:
977:
939:
779:
741:
1916:
1880:
1844:
1808:
1772:
1674:
1662:
1650:
1638:
3289:
853:
1832:
1820:
617:
1760:
1480:
6931:
inconsistent, as a similar interpretation is impossible for Cm and C+ (in Cm, m cannot possibly refer to the sixth, which is major by definition, and in C+, + cannot refer to the seventh, which is minor). Both approaches reveal only one of the intervals (M3 or M7), and require other rules to complete the task. Whatever is the decoding method, the result is the same (e.g., CM is always conventionally decoded as C–E–G–B, implying M3, P5, M7). The advantage of rule 1 is that it has no exceptions, which makes it the simplest possible approach to decode chord quality.
1754:
7735:. "Lewin posits the notion of musical 'spaces' made up of elements between which we can intuit 'intervals'....Lewin gives a number of examples of musical spaces, including the diatonic gamut of pitches arranged in scalar order; the 12 pitch classes under equal temperament; a succession of time-points pulsing at regular temporal distances one time unit apart; and a family of durations, each measuring a temporal span in time units....transformations of timbre are proposed that derive from changes in the spectrum of partials..."
3334:
2715:
1608:
1180:
2310:
5291:
8974:
1715:
two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (
3128:
1474:
1111:
2681:. Helmholtz then designated that two harmonic tones that shared common low partials would be more consonant, as they produced less beats. Helmholtz disregarded partials above the seventh, as he believed that they were not audible enough to have significant effect. From this Helmholtz categorises the octave, perfect fifth, perfect fourth, major sixth, major third, and minor third as consonant, in decreasing value, and other intervals as dissonant.
2860:
6716:
2402:
42:
8842:
2563:
1195:
6772:
3251:(also skhisma) is the difference between five octaves and eight justly tuned fifths plus one justly tuned major third. It is expressed by the ratio 32805:32768 (2.0 cents). It is also the difference between the Pythagorean and syntonic commas. (A schismic major third is a schisma different from a just major third, eight fifths down and five octaves up, F
1249:). This means that interval numbers can also be determined by counting diatonic scale degrees, rather than staff positions, provided that the two notes that form the interval are drawn from a diatonic scale. Namely, B—D is a third because in any diatonic scale that contains B and D, the sequence from B to D includes three notes. For instance, in the B-
6444:, the distance between two pitches upward or downward. For instance, the interval from C upward to G is 7, and the interval from G downward to C is −7. One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory.
5256:(augmented fourth or diminished fifth), could have other just ratios; for instance, 7:5 (about 583 cents) or 17:12 (about 603 cents) are possible alternatives for the augmented fourth (the latter is fairly common, as it is closer to the equal-tempered value of 600 cents). The 7:4 interval (about 969 cents), also known as the
5355:
using the letter "C", for cycle, with an interval-class integer to distinguish the interval. Thus the diminished-seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle.
153:
between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this
5317:
note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of
3664:
The quality of a compound interval is determined by the quality of the simple interval on which it is based. For instance, a compound major third is a major tenth (1+(8−1)+(3−1) = 10), or a major seventeenth (1+(8−1)+(8−1)+(3−1) = 17), and a compound perfect fifth is a perfect twelfth (1+(8−1)+(5−1)
1303:
Notice that interval numbers represent an inclusive count of encompassed staff positions or note names, not the difference between the endpoints. In other words, one starts counting the lower pitch as one, not zero. For that reason, the interval E–E, a perfect unison, is also called a prime (meaning
6933:
According to the two approaches, some may format the major seventh chord as CM (general rule 1: M refers to M3), and others as C (alternative approach: M refers to M7). Fortunately, even C becomes compatible with rule 1 if it is considered an abbreviation of CM, in which the first M is omitted. The
6486:
Notice that staff positions, when used to determine the conventional interval number (second, third, fourth, etc.), are counted including the position of the lower note of the interval, while generic interval numbers are counted excluding that position. Thus, generic interval numbers are smaller by
4140:
and the corresponding symbols 3 and 5 are typically omitted. This rule can be generalized to all kinds of chords, provided the above-mentioned qualities appear immediately after the root note, or at the beginning of the chord name or symbol. For instance, in the chord symbols Cm and Cm, m refers to
3364:
Any compound interval can be always decomposed into one or more octaves plus one simple interval. For instance, a major seventeenth can be decomposed into two octaves and one major third, and this is the reason why it is called a compound major third, even when it is built by adding up four fifths.
6751:
For example, an interval between two bell-like sounds, which have no pitch salience, is still perceptible. When two tones have similar acoustic spectra (sets of partials), the interval is just the distance of the shift of a tone spectrum along the frequency axis, so linking to pitches as reference
1714:
defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in
3998:
It is also worth mentioning here the major seventeenth (28 semitones)—an interval larger than two octaves that can be considered a multiple of a perfect fifth (7 semitones) as it can be decomposed into four perfect fifths (7 × 4 = 28 semitones), or two octaves plus a major third (12 + 12 + 4 = 28
5834:
The prefix semi- is typically used herein to mean "shorter", rather than "half". Namely, a semitonus, semiditonus, semidiatessaron, semidiapente, semihexachordum, semiheptachordum, or semidiapason, is shorter by one semitone than the corresponding whole interval. For instance, a semiditonus (3
6930:
General rule 1 achieves consistency in the interpretation of symbols such as CM, Cm, and C+. Some musicians legitimately prefer to think that, in CM, M refers to the seventh, rather than to the third. This alternative approach is legitimate, as both the third and seventh are major, yet it is
6447:
The interval between pitch classes may be measured with ordered and unordered pitch-class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered
2354:
The inversion of a major interval is a minor interval, and vice versa; the inversion of a perfect interval is also perfect; the inversion of an augmented interval is a diminished interval, and vice versa; the inversion of a doubly augmented interval is a doubly diminished interval, and vice
6953:, each spanning 3 semitones (m3 + m3), compatible with the definition of tertian chord. If a major third were used (4 semitones), this would entail a sequence containing a major second (M3 + M2 = 4 + 2 semitones = 6 semitones), which would not meet the definition of tertian chord.
2667:, it makes more sense to speak of consonant and dissonant chords, and certain intervals previously considered dissonant (such as minor sevenths) became acceptable in certain contexts. However, 16th-century practice was still taught to beginning musicians throughout this period.
6318:
Intervals in non-diatonic scales can be named using analogs of the diatonic interval names, by using a diatonic interval of similar size and distinguishing it by varying the quality, or by adding other modifiers. For example, the just interval 7/6 may be referred to as a
5232:
system uses just tones and semitones as building blocks, rather than a stack of perfect fifths, and this leads to even more varied intervals throughout the scale (each kind of interval has three or four different sizes). A more detailed analysis is provided at
3665:= 12) or a perfect nineteenth (1+(8−1)+(8−1)+(5−1) = 19). Notice that two octaves are a fifteenth, not a sixteenth (1+(8−1)+(8−1) = 15). Similarly, three octaves are a twenty-second (1+3×(8−1) = 22), four octaves are a twenty-ninth (1+3×(8-1) = 29), and so on.
3342:
2723:
6482:
are distinguished. Specific intervals are the interval class or number of semitones between scale steps or collection members, and generic intervals are the number of diatonic scale steps (or staff positions) between notes of a collection or scale.
6752:
points is not necessary. The same principle naturally applies to pitched tones (with similar harmonic spectra), which means that intervals can be perceived "directly" without pitch recognition. This explains in particular the predominance of
3153:
1734:
Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.
7377:, p. 182d: "Just as the coincidences of the two first upper partial tones led us to the natural consonances of the Octave and Fifth, the coincidences of higher upper partials would lead us to a further series of natural consonances."
3343:
2724:
1528:
Perfect intervals are so-called because they were traditionally considered perfectly consonant, although in
Western classical music the perfect fourth was sometimes regarded as a less than perfect consonance, when its function was
6724:
208:
5237:. 5-limit tuning was designed to maximize the number of just intervals, but even in this system some intervals are not just (e.g., 3 fifths, 5 major thirds and 6 minor thirds are not just; also, 3 major and 3 minor thirds are
2580:
6948:
chords (chords defined by sequences of thirds), and a major third would produce in this case a non-tertian chord. Namely, the diminished fifth spans 6 semitones from root, thus it may be decomposed into a sequence of two
2868:
1599:). Conversely, other kinds of intervals have the opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval.
2526:
depicts the 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale.
1932:. Diminished intervals, on the other hand, are narrower by one semitone than perfect or minor intervals of the same interval number: they are narrower by a chromatic semitone. For instance, an augmented sixth such as E
4153:
of an extra interval is specified immediately after chord quality, the quality of that interval may coincide with chord quality (e.g., CM = CM). However, this is not always true (e.g., Cm = Cm, C+ = C+, CM = CM). See
447:
3154:
1893:
1797:
1517:
1493:
1119:
1092:
818:
5248:. It is possible to construct juster intervals or just intervals closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular, the
5329:
seventh chord (possibly the dominant of the mediant V/iii). According to the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic.
1905:
1869:
1857:
1699:
1687:
1505:
1054:
1016:
902:
2658:
usage, perfect fifths and octaves, and major and minor thirds and sixths were considered harmonically consonant, and all other intervals dissonant, including the perfect fourth, which by 1473 was described (by
2377:
For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of a 5:4 ratio is an 8:5 ratio.
5107:, the intervals are never precisely in tune with each other. This is the price of using equidistant intervals in a 12-tone scale. For simplicity, for some types of interval the table shows only one value (the
3228:
is generally used to mean the difference between three justly tuned major thirds and one octave. It is expressed by the ratio 128:125 (41.1 cents). However, it has been used to mean other small intervals: see
2514:
1785:
1627:
1615:
704:
661:
5159:), and their average size is 400 cents. In short, similar differences in width are observed for all interval types, except for unisons and octaves, and they are all multiples of ε (the difference between the
3539:
1917:
1881:
1845:
1809:
1773:
1675:
1663:
1651:
1639:
1533:. Conversely, minor, major, augmented, or diminished intervals are typically considered less consonant, and were traditionally classified as mediocre consonances, imperfect consonances, or near-dissonances.
978:
940:
780:
742:
7577:
Le
Istitutione harmoniche ... nelle quali, oltre le materie appartenenti alla musica, si trovano dichiarati molti luoghi di Poeti, d'Historici e di Filosofi, si come nel leggerle si potrà chiaramente vedere
6333:
interval. These names refer just to the individual interval's size, and the interval number need not correspond to the number of scale degrees of a (heptatonic) scale. This naming is particularly common in
6725:
3115:
may not necessarily coincide. These two notes are enharmonic in 12-TET, but may not be so in another tuning system. In such cases, the intervals they form would also not be enharmonic. For example, in
229:
The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to a different context: frequency ratios or cents.
3659:
3290:
1833:
1821:
854:
306:. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an
2815:
More generally, a step is a smaller or narrower interval in a musical line, and a skip is a wider or larger interval, where the categorization of intervals into steps and skips is determined by the
3357:
In general, a compound interval may be defined by a sequence or "stack" of two or more simple intervals of any kind. For instance, a major tenth (two staff positions above one octave), also called
2579:
1761:
1481:
618:
6363:, respectively narrower than a minor or wider than a major interval. The exact size of such intervals depends on the tuning system, but they often vary from the diatonic interval sizes by about a
1928:
Augmented intervals are wider by one semitone than perfect or major intervals, while having the same interval number (i.e., encompassing the same number of staff positions): they are wider by a
530:
The names listed here cannot be determined by counting semitones alone. The rules to determine them are explained below. Other names, determined with different naming conventions, are listed in
2867:
2530:
The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E
7327:
5135: ≈ 3.42 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of about 738 cents (700 + 11
4225:(e.g., C = C) and contains, together with the implied major triad, one or more of the following extra intervals: minor 7th, major 9th, perfect 11th, and major 13th (see names and symbols for
1120:
2513:
6934:
omitted M is the quality of the third, and is deduced according to rule 2 (see above), consistently with the interpretation of the plain symbol C, which by the same rule stands for CM.
3999:
semitones). Intervals larger than a major seventeenth seldom come up, most often being referred to by their compound names, for example "two octaves plus a fifth" rather than "a 19th".
1328:
is only two staff positions above E, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance, the intervals B—D and D—F
1368:
4184:, the third must be minor. This rule overrides rule 2. For instance, Cdim implies a diminished 5th by rule 1, a minor 3rd by this rule, and a diminished 7th by definition (see below).
2677:. Helmholtz further believed that the beating produced by the upper partials of harmonic sounds was the cause of dissonance for intervals too far apart to produce beating between the
2374:
Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded".
5260:, has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. For further details about reference ratios, see
310:
fifth has a frequency ratio of 2:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between the size of intervals in different tuning systems, see
4155:
4105:
2578:
1284:
to the notes that form an interval, by definition the notes do not change their staff positions. As a consequence, any interval has the same interval number as the corresponding
2866:
2559:
scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth.
3340:
2721:
7380:
2588:
The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called
7315:
7274:(New York: St Martin's Press; London: G. Bell, 1957): , reprinted 1966, 1970, and 1976 by G. Bell, 1971 by St Martins Press, 1981, 1984, and 1986 London: Bell & Hyman.
4141:
the interval m3, and 3 is omitted. When these qualities do not appear immediately after the root note, or at the beginning of the name or symbol, they should be considered
2515:
3171:
There are also a number of minute intervals not found in the chromatic scale or labeled with a diatonic function, which have names of their own. They may be described as
1218:) because the notes from B to the D above it encompass three letter names (B, C, D) and occupy three consecutive staff positions, including the positions of B and D. The
3242:
is the difference between three octaves and four justly tuned perfect fifths plus two justly tuned major thirds. It is expressed by the ratio 2048:2025 (19.6 cents).
3151:
2643:
are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be
7588:
4136:
always refer to the interval of the fifth above root. The same is true for the corresponding symbols (e.g., Cm means C, and C+ means C). Thus, the terms third and
6722:
5321:
As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (
5207: ≈ 1.96 cents, the difference between the Pythagorean fifth and the average fifth). Notice that here the fifth is wider than 700 cents, while in most
2735:
above). Intervals spanning more than one octave are called compound intervals, as they can be obtained by adding one or more octaves to a simple interval (see
4173:) are implied. For instance, a C chord is a C major triad, and the name C minor seventh (Cm) implies a minor 3rd by rule 1, a perfect 5th by this rule, and a
2691:, in which an interval's strength, consonance, or stability is determined by its approximation to a lower and stronger, or higher and weaker, position in the
378:
4215:
2890:
spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of
2037:
is a fifth, as it encompasses five staff positions (C, D, E, F, G), and it is diminished, as it falls short of a perfect fifth (such as C-G) by one semitone.
3341:
2722:
4230:
2544:) is considered diatonic if the harmonic minor scales are considered diatonic as well. Otherwise, it is considered chromatic. For further details, see the
2325:
or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.
5819:
was used as an official language throughout Europe for scientific and music textbooks. In music, many
English terms are derived from Latin. For instance,
4226:
8876:
2313:
Major 13th (compound major 6th) inverts to a minor 3rd by moving the bottom note up two octaves, the top note down two octaves, or both notes one octave.
1117:
3350:
A compound interval is an interval spanning more than one octave. Conversely, intervals spanning at most one octave are called simple intervals (see
2052:
is a third, as it encompasses three staff positions (C, D, E), and it is doubly augmented, as it exceeds a major third (such as C-E) by two semitone.
2028:
is a fourth, as it encompasses four staff positions (C, D, E, F), and it is augmented, as it exceeds a perfect fourth (such as C-F) by one semitone.
3152:
5799:
Additionally, some cultures around the world have their own names for intervals found in their music. For instance, 22 kinds of intervals, called
1214:(lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval B—D is a third (denoted
7671:
7300:
7012:
5835:
semitones, or about 300 cents) is not half of a ditonus (4 semitones, or about 400 cents), but a ditonus shortened by one semitone. Moreover, in
3307:
is the amount that two major thirds of 5:4 and a septimal major third, or supermajor third, of 9:7 exceeds the octave. Ratio 225:224 (7.7 cents).
3210:
is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80 (21.5 cents).
6723:
495:
Intervals with different names may span the same number of semitones, and may even have the same width. For instance, the interval from D to F
5313:. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its
8563:
6323:, since it is ~267 cents wide, which is narrower than a minor third (300 cents in 12-TET, ~316 cents for the just interval 6/5), or as the
4025:
is a chord containing three notes defined by the root and two intervals (major third and perfect fifth). Sometimes even a single interval (
4012:
3088:, these intervals are indistinguishable to the ear, because they are all played with the same two keys. However, in a musical context, the
2581:
185:. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G
4017:
Chords are sets of three or more notes. They are typically defined as the combination of intervals starting from a common note called the
2869:
2663:) as dissonant, except between the upper parts of a vertical sonority—for example, with a supporting third below ("6-3 chords"). In the
7622:, edited and translated by Peter M. Lefferts. Greek & Latin Music Theory 7 (Lincoln: University of Nebraska Press, 1991): 193fn17.
352:
have the same size, the size of one semitone is exactly 100 cents. Hence, in 12-TET the cent can be also defined as one hundredth of a
7602:, abbreviationes et index fontium composuit C. van de Kieft, adiuvante G. S. M. M. Lake-Schoonebeek (Leiden: E. J. Brill, 1976): 955.
3406:
1118:
2829:
in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called
7336:, p. 178: "The cause of this phenomenon must be looked for in the beats produced by the high upper partials of such compound tones".
5364:
As shown below, some of the above-mentioned intervals have alternative names, and some of them take a specific alternative name in
7864:
Lissajous Curves: Interactive simulation of graphical representations of musical intervals, beats, interference, vibrating strings
8869:
6379:
for seconds, thirds, sixths, and sevenths. This naming convention can be extended to unisons, fourths, fifths, and octaves with
6437:. In this system, intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6.
7253:, 16th edition. London: Augener & Co. (facsimile reprint, St. Clair Shores, Michigan: Scholarly Press, 1970), p. 10.
3550:
2405:
45:
7757:
7712:
7684:
7121:
7075:
7025:
5351:, "unfold a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by
1426:). It is possible to have doubly diminished and doubly augmented intervals, but these are quite rare, as they occur only in
5415:, three of which meet the definition of diminished second, and hence are listed in the table below. The fourth one, called
181:. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is
5839:(the most commonly used tuning system up to the 16th century), a semitritonus (d5) is smaller than a tritonus (A4) by one
2381:
For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.
7906:
6375:, in 24-TET is 150 cents, exactly halfway between a minor second and major second. Combined, these yield the progression
2333:
211:
122:. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called
8862:
7051:
6984:
8065:
7732:
7607:
7600:
Mediae latinitatis lexicon minus: Lexique latin médiéval–français/anglais: A Medieval Latin–French/English
Dictionary
7563:
7523:
7499:
7478:
7451:
7415:
7374:
7287:
7279:
7258:
7187:
7155:
7042:
Aldwell, E.; Schachter, C.; Cadwallader, A. (11 March 2010), "Part 1: The
Primary Materials and Procedures, Unit 1",
5099:
type of interval (including the semitone) changes depending on the note that starts the interval. This is the art of
114:. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a
9105:
7707:, for example sections 3.3.1 and 5.4.2. New Haven: Yale University Press. Reprinted Oxford University Press, 2007.
6945:
165:
In
Western music theory, the most common naming scheme for intervals describes two properties of the interval: the
17:
4029:) is considered a chord. Chords are classified based on the quality and number of the intervals that define them.
7389:, p. 183: "Here I have stopped, because the 7th partial tone is entirely eliminated, or at least much weakened.".
5252:
of the 5-limit tuning scale provides a juster value for the minor seventh (9:5, rather than 16:9). Moreover, the
5170:
5073:
In this table, the interval widths used in four different tuning systems are compared. To facilitate comparison,
2351:
The interval number and the number of its inversion always add up to nine (4 + 5 = 9, in the example just given).
7324:, p. 172: "The roughness from sounding two tones together depends... the number of beats produced in a second.".
2897:
For example, the four intervals listed in the table below are all enharmonically equivalent, because the notes F
2388:
is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.
7627:
5192:-comma meantone was designed to produce just major thirds, but only 8 of them are just (5:4, about 386 cents).
4260:
font can be deduced from chord name or symbol by applying rule 1. In symbol examples, C is used as chord root.
6979:(30th edition, revised and largely rewritten ed.), London: Augener; Boston: Boston Music Co., p. 1,
5244:
The above-mentioned symmetric scale 1, defined in the 5-limit tuning system, is not the only method to obtain
4526:
4054:
3219:
is 64:63 (27.3 cents), and is the difference between the
Pythagorean or 3-limit "7th" and the "harmonic 7th".
2506:
8355:
8335:
2401:
484:
is an interval spanning three tones, or six semitones (for example, an augmented fourth). Rarely, the term
41:
8461:
7666:
7309:
7007:
5222:
2329:
207:
7089:
5420:
9241:
8467:
7879:
6795:
3197:
is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the
302:
Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called
8028:
7991:
7857:
2408:
48:
8885:
8250:
7593:
5400:
4149:), m is the chord quality and refers to the m3 interval, while M refers to the M7 interval. When the
4146:
3096:
2640:
2635:
1238:
303:
31:
5221:-comma meantone, it is tempered to a size smaller than 700. A more detailed analysis is provided at
7830:
7435:
4497:
4050:
2396:
Intervals can be described, classified, or compared with each other according to various criteria.
5261:
1430:
contexts. The combination of number (or generic interval) and quality (or modifier) is called the
9072:
8963:
8845:
8583:
8522:
7899:
7620:
Robert De Handlo: The Rules, and
Johannes Hanboys, The Summa: A New Critical Text and Translation
7443:
7147:
6800:
6353:
6313:
5295:
5249:
5234:
5078:
4580:
4568:
4470:
2769:, is a linear interval between two consecutive notes of a scale. Any larger interval is called a
2692:
2347:
There are two rules to determine the number and quality of the inversion of any simple interval:
2336:
1596:
456:
The table shows the most widely used conventional names for the intervals between the notes of a
214:
4065:
used for chord quality are similar to those used for interval quality (see above). In addition,
8643:
8120:
7776:(1994). "A principle of correlativity of perception and its application to music recognition".
6915:
6441:
6412:
5804:
5464:
5389:
5373:
5115:
4592:
4398:
3116:
2664:
2545:
2471:
2304:
1723:). Conversely, since neither kind of third is perfect, the larger one is called "major third" (
1588:
7937:
5407:
the diminished second is a descending interval (524288:531441, or about −23.5 cents), and the
1979:) are the only augmented and diminished intervals that appear in diatonic scales (see table).
1300:(spanning 2 semitones) are thirds, like the corresponding natural interval B—D (3 semitones).
8638:
8449:
7816:
7357:
6883:
6805:
6422:
6391:. This allows one to name all intervals in 24-TET or 31-TET, the latter of which was used by
5770:
2678:
2670:
1991:
alone. As explained above, the number of staff positions must be taken into account as well.
464:(also known as perfect prime) is an interval formed by two identical notes. Its size is zero
6440:
In atonal or musical set theory, there are numerous types of intervals, the first being the
5412:
1304:"1"), even though there is no difference between the endpoints. Continuing, the interval E–F
9098:
8825:
8578:
8485:
8479:
7826:
7676:
7366:
7017:
6911:
6886:
thereof. In other words, a scale that can be written using seven consecutive notes without
6753:
6421:
theory, originally developed for equal-tempered
European classical music written using the
6325:
5208:
3100:
2541:
2239:
1403:
1355:
This scheme applies to intervals up to an octave (12 semitones). For larger intervals, see
87:
if it refers to successively sounding tones, such as two adjacent pitches in a melody, and
7868:
5127:, by definition 11 perfect fifths have a size of approximately 697 cents (700 −
1753:
340:, and along that scale the distance between a given frequency and its double (also called
8:
8951:
8608:
8473:
8455:
7852:
7643:
6907:
6903:
6815:
6471:
5606:
4445:
4420:
2696:
1748:
1250:
182:
7752:. Lecture Notes in Artificial Intelligence. Vol. 746. Berlin-Heidelberg: Springer.
2620:
are not contained in the C major scale. However, it is diatonic to others, such as the A
1556:), with five and seven semitones respectively. One occurrence of a fourth is augmented (
8956:
8721:
8158:
7892:
7820:
7795:
7361:
7094:
6887:
6434:
6180:
5836:
5454:
5404:
5365:
5196:
4585:
4236:
If the number is 5, the chord (technically not a chord in the traditional sense, but a
3842:
2660:
1929:
1744:
1449:
is the quality of the simple interval on which it is based. Some other qualifiers like
1288:
interval, formed by the same notes without accidentals. For instance, the intervals B–D
1281:
963:
523:), these intervals also have the same width. Namely, all semitones have a width of 100
516:
252:
8777:
5169:-comma meantone fifth and the average fifth). A more detailed analysis is provided at
8663:
8603:
8164:
8140:
8128:
8109:
7923:
7863:
7844:
7753:
7728:
7708:
7680:
7623:
7603:
7559:
7519:
7511:
7495:
7474:
7447:
7411:
7370:
7283:
7275:
7254:
7183:
7151:
7117:
7071:
7047:
7021:
6980:
6498:
6475:
6461:
6396:
6285:
6250:
6007:
5840:
5579:
5525:
5513:
5408:
5369:
5322:
5156:
5108:
5104:
4608:
4254:), and some of the symbols used to denote them. The interval qualities or numbers in
3193:
3089:
3021:
2655:
2537:
2318:
1077:
1039:
765:
603:
520:
512:
345:
337:
333:
307:
344:) is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone
9189:
9174:
9157:
8906:
8896:
8733:
8558:
8503:
8497:
8491:
8395:
8295:
8268:
8152:
8134:
8079:
8073:
7787:
7778:
7773:
7745:
6867:
6785:
6732:
The term "interval" can also be generalized to other music elements besides pitch.
6503:
6479:
6465:
6430:
6346:
6309:
6110:
5972:
5942:
5741:
5720:
5591:
5343:
5275:
5257:
5144:
4373:
4199:
4181:
4133:
3811:
3736:
3303:
3132:
3054:
2674:
2128:
2094:
887:
727:
684:
641:
7212:
3333:
2714:
2242:, followed by the interval number. The indications M and P are often omitted. The
9194:
9169:
9091:
8820:
8701:
8425:
8213:
8103:
8097:
8085:
6335:
6215:
6145:
6042:
5419:(81:80) can neither be regarded as a diminished second, nor as its opposite. See
5381:
5326:
5245:
5100:
5092:
4352:
4129:
4046:
3855:
3776:
3179:, as they describe small discrepancies, observed in some tuning systems, between
2748:
2499:
2223:
2215:
2164:
1994:
For example, as shown in the table below, there are six semitones between C and F
1987:
Neither the number, nor the quality of an interval can be determined by counting
1607:
1595:
of the two notes, it hardly affects their level of consonance (matching of their
1395:
1387:
1285:
1260:
1001:
925:
803:
457:
256:
103:
7144:
The
Complete Musician: An Integrated Approach to Theory, Analysis, and Listening
5199:
is characterized by smaller differences because they are multiples of a smaller
4202:(e.g., C = C = C) and contains, together with the implied major triad, an extra
2317:
A simple interval (i.e., an interval smaller than or equal to an octave) may be
9147:
9003:
8941:
8681:
8675:
8669:
8441:
7968:
7535:
7246:
6972:
6863:
6757:
6516:
6449:
6408:
6392:
6368:
5800:
5697:
5493:
5459:
5416:
5385:
5348:
5339:
5306:
5229:
4222:
4207:
4058:
3215:
3206:
3139:
3085:
2935:
2826:
2816:
2782:
2552:
2488:
2385:
2067:
1711:
1591:
of a perfect interval is also perfect. Since the inversion does not change the
1537:
1438:(sometimes used only for intervals appearing in the diatonic scale), or simply
1372:
1246:
1242:
1211:
1187:
795:
595:
519:
is tuned so that the 12 notes of the chromatic scale are equally spaced (as in
461:
280:
260:
238:
150:
146:. Intervals can be arbitrarily small, and even imperceptible to the human ear.
111:
7873:
2309:
488:
is also used to indicate an interval spanning two whole tones (for example, a
9235:
9220:
9179:
9162:
9152:
9059:
9054:
9008:
8931:
8916:
8805:
8654:
8573:
8568:
8514:
8375:
8315:
8201:
8189:
8054:
8017:
7974:
7662:
7542:. New York: Associated Music Publishers. Cited in Cope (1997), p. 40–41.
7492:
A Player's Guide to Chords and Harmony: Music Theory for Real-World Musicians
7305:
7230:
7003:
6895:
6891:
6810:
5760:
5707:
5686:
5661:
5636:
5411:
is its opposite (531441:524288, or about 23.5 cents). 5-limit tuning defines
5396:
5238:
5074:
4904:
4896:
4820:
4812:
4777:
4741:
4267:
4174:
4166:
4137:
4113:
4008:
3283:
3176:
3162:
2887:
2556:
1316:
is only one staff position, or diatonic-scale degree, above E. Similarly, E—G
1183:
1179:
1031:
993:
879:
276:
178:
127:
123:
96:
72:
8854:
6719:
Division of the measure/chromatic scale, followed by pitch/time-point series
5290:
4095:
9215:
9044:
9039:
8926:
8772:
8633:
8279:
8036:
7999:
7551:
6871:
6790:
6777:
6372:
6364:
5621:
5556:
5399:
is a diminished second, but this is not always true (for more details, see
5352:
5301:
Although intervals are usually designated in relation to their lower note,
4280:
4237:
4203:
4192:
4125:
4062:
4026:
4018:
3321:
3312:
3184:
2794:
2786:
2566:
2365:
above it is a minor third. By the two rules just given, the interval from E
1530:
1128:
676:
633:
524:
477:
465:
329:
323:
155:
107:
64:
9204:
9018:
9013:
8998:
8993:
8946:
8782:
8613:
8048:
8042:
8011:
8005:
7700:
7431:
7179:
6950:
6899:
6879:
6875:
6733:
5674:
5649:
5279:
4331:
4297:
4241:
4211:
4170:
4162:
4121:
4117:
4042:
4038:
4022:
3789:
3768:
3749:
3728:
3267:
3127:
2959:
2820:
2809:
2802:
2650:
These terms are relative to the usage of different compositional styles.
1592:
1473:
1204:
955:
917:
757:
719:
502:
489:
288:
284:
272:
174:
7822:
On the Sensations of Tone as a Theoretical Basis for the Theory of Music
7799:
7362:
On the Sensations of Tone as a Theoretical Basis for the Theory of Music
1110:
442:{\displaystyle n=1200\cdot \log _{2}\left({\frac {f_{2}}{f_{1}}}\right)}
259:
tuning system, the size of the main intervals can be expressed by small-
8901:
8815:
8709:
8207:
7403:
7002:
Lindley, Mark; Campbell, Murray; Greated, Clive (2001). "Interval". In
6906:
scales, but does not include some other seven-tone scales, such as the
6741:
6339:
5630:
5541:
5302:
5269:
5140:
4177:
by definition (see below). This rule has one exception (see next rule).
3928:
3902:
3882:
3868:
3238:
3180:
2878:
2854:
2684:
2250:
is usually referred to simply as "a unison" but can be labeled P1. The
2231:
1564:), both spanning six semitones. For instance, in an E-major scale, the
1411:
1222:
and the figure above show intervals with numbers ranging from 1 (e.g.,
692:
473:
311:
131:
6840:
is sometimes used more strictly as a synonym of augmented fourth (A4).
2706:
All of the above analyses refer to vertical (simultaneous) intervals.
9210:
8715:
8219:
7875:
Just intervals, from the unison to the octave, played on a drone note
7791:
6426:
6418:
4552:
3987:
3962:
3948:
3198:
3172:
3166:
3095:
The discussion above assumes the use of the prevalent tuning system,
2859:
1988:
1427:
1367:
248:
159:
119:
7518:, p. 63. Hammondsworth (England), and New York: Penguin Books.
7369:(1885) reprinted by Dover Publications with new introduction (1954)
6715:
4250:
The table shows the intervals contained in some of the main chords (
3119:, all four intervals shown in the example above would be different.
2673:(1821–1894) theorised that dissonance was caused by the presence of
2551:
By a commonly used definition of diatonic scale (which excludes the
1340:), not a sixth. Similarly, a stack of three thirds, such as B—D, D—F
9126:
8936:
8747:
8195:
7943:
5820:
5564:
5088:
5083:
4256:
4195:
and a number (e.g., "C seventh", or C) are interpreted as follows:
3798:
3678:
3317:
2891:
2482:
649:
550:
472:
is any interval between two adjacent notes in a chromatic scale, a
469:
353:
349:
115:
6377:
diminished, subminor, minor, neutral, major, supermajor, augmented
4244:. Only the root, a perfect fifth and usually an octave are played.
3131:
Pythagorean comma on C; the note depicted as lower on the staff (B
2731:
A simple interval is an interval spanning at most one octave (see
9142:
9132:
9049:
8911:
8753:
8741:
8727:
8146:
8091:
7725:
Repetition in Music: Theoretical and Metatheoretical Perspectives
6837:
6330:
5728:
5253:
3859:
3262:
3247:
2562:
2443:
2429:
2251:
1259:–D. This is not true for all kinds of scales. For instance, in a
866:
843:
835:
481:
359:
Mathematically, the size in cents of the interval from frequency
243:
The size of an interval between two notes may be measured by the
3534:{\displaystyle DN_{c}=1+(DN_{1}-1)+(DN_{2}-1)+...+(DN_{n}-1),\ }
9199:
9184:
9114:
9023:
8988:
8810:
8787:
8695:
8689:
7980:
7962:
6745:
5783:
5533:
3279:
3230:
3224:
2450:
2433:
2322:
2247:
2243:
1194:
1069:
485:
341:
268:
264:
7068:
How Equal Temperament Ruined Harmony (and Why You Should Care)
5147:); 8 major thirds have size about 386 cents (400 − 4
2808:
For example, C to D (major second) is a step, whereas C to E (
1378:
The name of any interval is further qualified using the terms
95:
if it pertains to simultaneously sounding tones, such as in a
8183:
5816:
3715:
527:, and all intervals spanning 4 semitones are 400 cents wide.
244:
7884:
3092:
of the notes these intervals incorporate is very different.
579:
531:
7041:
6138:
hexachordum minus, semitonus maius cum diapente, tetratonus
1956:–C spans seven semitones, falling short of a minor sixth (E
1210:
The number of an interval is the number of letter names or
7558:, p. 21. California: University of California Press.
5359:
224:
Example: Minor third on D in equal temperament: 300 cents.
9083:
6898:, or with no signature. This includes, for instance, the
4096:
Deducing component intervals from chord names and symbols
4032:
2407:
Audio playback is not supported in your browser. You can
2335:
Audio playback is not supported in your browser. You can
1548:) are perfect. Most fourths and fifths are also perfect (
328:
The standard system for comparing interval sizes is with
312:§ Size of intervals used in different tuning systems
213:
Audio playback is not supported in your browser. You can
47:
Audio playback is not supported in your browser. You can
7339:
6208:
heptachordum minus, semiditonus cum diapente, pentatonus
3654:{\displaystyle DN_{c}=DN_{1}+DN_{2}+...+DN_{n}-(n-1),\ }
1269:–D. This is the reason interval numbers are also called
291:). Intervals with small-integer ratios are often called
7176:
Tonal Harmony, with an Introduction to Post-Tonal Music
6740:
uses interval as a generic measure of distance between
5267:
In the diatonic system, every interval has one or more
1950:—C) by one semitone, while a diminished sixth such as E
106:
music, intervals are most commonly differences between
7410:, pp. 40–41. New York, New York: Schirmer Books.
7001:
6487:
1, with respect to the conventional interval numbers.
5392:(or epimoric ratio). The same is true for the octave.
3286:), with a frequency ratio of 15625:15552 (8.1 cents) (
2258:. The interval qualities may be also abbreviated with
1719:), the 6-semitone fifth is called "diminished fifth" (
1334:
are thirds, but joined together they form a fifth (B—F
476:
is an interval spanning two semitones (for example, a
7174:
Kostka, Stefan; Payne, Dorothy; Almén, Byron (2018).
6997:
6995:
6710:
4198:
If the number is 2, 4, 6, etc., the chord is a major
3553:
3409:
2453:
if they sound successively. Melodic intervals can be
381:
126:, and describe small discrepancies, observed in some
7116:(1st ed.). New York: W. W. Norton. p. 55.
6767:
6367:(50 cents, half a chromatic step). For example, the
4145:, rather than chord qualities. For instance, in Cm (
4124:
always refer to the interval of the third above the
3183:
notes. In the following list, the interval sizes in
2498:
is a non-diatonic interval formed by two notes of a
336:
unit of measurement. If frequency is expressed in a
173:(unison, second, third, etc.). Examples include the
75:
between two sounds. An interval may be described as
7772:
7744:
4104:are summarized below. Further details are given at
2909:
indicate the same pitch, and the same is true for A
2254:, an augmented fourth or diminished fifth is often
169:(perfect, major, minor, augmented, diminished) and
7066:Duffin, Ross W. (2007), "3. Non-keyboard tuning",
6992:
6345:The most common of these extended qualities are a
4553:Size of intervals used in different tuning systems
4221:If the number is 7, 9, 11, 13, etc., the chord is
3653:
3533:
2845:melodic motions, characterized by frequent skips.
441:
7705:Generalized Musical Intervals and Transformations
7098:. Oxford University Press. Accessed August 2013.
6738:Generalized Musical Intervals and Transformations
6455:
5372:, or meantone temperament tuning systems such as
5151:), 4 have size about 427 cents (400 + 8
492:), or more strictly as a synonym of major third.
9233:
7173:
7112:Burstein, L. Poundie; Straus, Joseph N. (2016).
7672:The New Grove Dictionary of Music and Musicians
7638:
7636:
7301:The New Grove Dictionary of Music and Musicians
7013:The New Grove Dictionary of Music and Musicians
2753:Linear (melodic) intervals may be described as
1944:spans ten semitones, exceeding a major sixth (E
118:. Intervals smaller than a semitone are called
7430:
7111:
1105:
515:. However, they both span 4 semitones. If the
9099:
8884:
8870:
7900:
7738:
6352:, in between a minor and major interval; and
3175:, and some of them can be also classified as
2510:Ascending and descending chromatic scale on C
1163:) describes the quality of the interval, and
7633:
4187:Names and symbols that contain only a plain
4013:Chord names and symbols (jazz and pop music)
1230:). Intervals with larger numbers are called
7766:
7750:Artificial Perception and Music Recognition
7426:
7424:
6870:, which is either a sequence of successive
6832:
6830:
6293:
6276:
6258:
6241:
6223:
6206:
6188:
6171:
6153:
6136:
6118:
6101:
6083:
6068:
6050:
6033:
6015:
5998:
5980:
5963:
5933:
5915:
5900:
5882:
5825:
5223:Pythagorean tuning § Size of intervals
5095:tuning systems, by definition the width of
2921:. All these intervals span four semitones.
1738:
1462:
1371:Intervals formed by the notes of a C major
1241:between staff positions and diatonic-scale
542:(compound intervals) are introduced below.
9106:
9092:
8877:
8863:
8841:
7907:
7893:
7661:Roeder, John (2001). "Interval Class". In
6858:
6856:
6854:
6852:
6850:
6848:
6846:
6389:diminished, sub, perfect, super, augmented
3668:
2629:
7815:
7386:
7345:
7333:
7321:
6395:. Various further extensions are used in
6303:
3361:, spans one octave plus one major third.
3103:, the pitches of pairs of notes such as F
2465:
2371:to the C above it must be a major sixth.
2359:For example, the interval from C to the E
1757:Augmented and diminished intervals on C:
1263:, there are four notes from B to D: B–C–C
1155:) is an interval name, in which the term
30:For albums or bands named Intervals, see
8175:
7465:
7463:
7421:
7201:
7199:
6926:
6924:
6827:
6714:
6402:
6243:heptachordum maius, ditonus cum diapente
5289:
5262:5-limit tuning § The justest ratios
5091:to integers. Notice that in each of the
4575:Comparison of interval width (in cents)
3332:
3126:
2858:
2713:
2561:
2505:
2487:is an interval formed by two notes of a
2308:
1752:
1606:
1472:
1366:
1193:
1178:
1131:, an interval is named according to its
1109:
154:reason, intervals are often measured in
7869:Elements of Harmony: Vertical Intervals
7408:Techniques of the Contemporary Composer
7399:
7397:
7395:
6843:
5360:Alternative interval naming conventions
5235:5-limit tuning § Size of intervals
4216:names and symbols for added tone chords
4106:Rules to decode chord names and symbols
3379:simple intervals with diatonic numbers
2848:
2736:
2457:(lower pitch precedes higher pitch) or
2423:
2206:Intervals are often abbreviated with a
1446:
1356:
1253:diatonic scale, the three notes are B–C
1231:
539:
348:(12-TET), a tuning system in which all
14:
9234:
8265:
7660:
7065:
6748:, or more abstract musical phenomena.
4033:Chord qualities and interval qualities
4002:
2709:
149:In physical terms, an interval is the
27:Difference in pitch between two sounds
9087:
8858:
7888:
7545:
7471:A History of Music in Western Culture
7460:
7365:, 2nd English edition, translated by
7210:
7196:
7169:
7167:
7141:
7114:Concise Introduction to Tonal Harmony
7046:(4th ed.), Schirmer, p. 8,
6971:
6938:
6921:
6173:hexachordum maius, tonus cum diapente
5810:
5727:
5520:
5450:
3328:
3142:) is slightly higher in pitch (than C
2446:if the two notes sound simultaneously
2201:
1352:—A, is a seventh (B-A), not a ninth.
832:
535:
7505:
7392:
7137:
7135:
7133:
7083:
5421:Diminished seconds in 5-limit tuning
3084:When played as isolated chords on a
7298:Drabkin, William (2001). "Fourth".
6433:is often used, most prominently in
5815:Up to the end of the 18th century,
5077:as provided by 5-limit tuning (see
4092:alone is not used for diminished).
3375:of a compound interval formed from
3351:
3122:
2732:
2596:. For instance, the perfect fifth A
1219:
232:
24:
7644:"Extended-diatonic interval names"
7270:See for example William Lovelock,
7237:, p. 21. First edition, 1984.
7164:
6711:Generalizations and non-pitch uses
5333:
5087:font, and the values in cents are
3324:. It is equal to exactly 50 cents.
3099:("12-TET"). But in other historic
2742:
2700:
2608:is chromatic to C major, because A
2305:Inversion (music) § Intervals
1727:), the smaller one "minor third" (
1602:
25:
9253:
7837:
7130:
6371:, the characteristic interval of
5843:(about a quarter of a semitone).
5180:-comma meantone Size of intervals
3201:ratio 531441:524288 (23.5 cents).
2863:Enharmonic tritones: A4 = d5 on C
2592:. All other intervals are called
2391:
451:
8972:
8840:
7540:The Craft of Musical Composition
7251:Harmony: Its Theory and Practice
6977:Harmony, Its Theory and Practice
6866:is herein strictly defined as a
6770:
6720:
5401:Alternative definitions of comma
5376:. All the intervals with prefix
5285:
4161:Without contrary information, a
3338:
3149:
2886:, if they both contain the same
2864:
2719:
2576:
2511:
2438:An interval can be described as
1611:Major and minor intervals on C:
1273:, and this convention is called
1115:
7717:
7694:
7654:
7613:
7582:
7569:
7529:
7484:
7351:
7292:
7264:
7240:
7224:
4191:(e.g., "seventh chord") or the
4100:The main rules to decode chord
3337:Simple and compound major third
3320:, which is half the width of a
2718:Simple and compound major third
2687:(1997) suggests the concept of
2291:d5 (or dim5): diminished fifth,
2288:A4 (or aug4): augmented fourth,
1560:) and one fifth is diminished (
7774:Tanguiane (Tangian), Andranick
7746:Tanguiane (Tangian), Andranick
7105:
7070:(1st ed.), W. W. Norton,
7059:
7035:
6965:
6456:Generic and specific intervals
5325:by popular terminology), or a
3642:
3630:
3544:which can also be written as:
3522:
3500:
3482:
3460:
3454:
3432:
3266:is the difference between six
2837:melodic motion, as opposed to
2418:Melodic and harmonic intervals
2321:by raising the lower pitch an
1294:(spanning 4 semitones) and B–D
1137:diatonic number, interval size
58:Melodic and harmonic intervals
13:
1:
7914:
6959:
6490:
5803:, are canonically defined in
4527:Half-diminished seventh chord
4037:The main chord qualities are
4021:of the chord. For instance a
2876:Two intervals are considered
2294:P5 (or perf5): perfect fifth.
7304:, second edition, edited by
5854:
5442:
5309:both suggest the concept of
4142:
3694:
3683:
2523:
2404:
2332:
2298:
1975:) and the diminished fifth (
566:
555:
210:
166:
44:
7:
8462:septimal chromatic semitone
6763:
6448:pitch-class intervals, see
6387:, yielding the progression
5858:
5446:
5388:, shown in the table, is a
5064:
5059:
5054:
5049:
5033:
5030:
5027:
5020:
5002:
4999:
4994:
4987:
4969:
4966:
4963:
4956:
4938:
4933:
4930:
4925:
4909:
4901:
4891:
4884:
4866:
4861:
4856:
4847:
4825:
4817:
4807:
4800:
4782:
4772:
4767:
4762:
4746:
4738:
4733:
4726:
4708:
4705:
4700:
4693:
4675:
4672:
4669:
4662:
4642:
4637:
4632:
4627:
4188:
4180:When the fifth interval is
4150:
2801:), with all intervals of a
2282:m2 (or min2): minor second,
1106:Interval number and quality
538:(commas or microtones) and
170:
10:
9258:
9113:
8468:septimal diatonic semitone
8256:(Numbers in brackets refer
7846:Essentials of Music Theory
7809:
7178:(8th ed.). New York:
7146:(4th ed.). New York:
6975:(1903), "I-Introduction",
6878:, C–D–E–F–G–A–B, or the A-
6796:List of meantone intervals
6703:
6689:
6675:
6661:
6647:
6633:
6617:
6601:
6587:
6573:
6559:
6545:
6531:
6459:
6406:
6307:
6070:semidiapente, semitritonus
5337:
5041:
5010:
4977:
4946:
4917:
4874:
4833:
4790:
4754:
4716:
4683:
4652:
4619:
4006:
3160:
2852:
2746:
2633:
2469:
2427:
2302:
2285:M3 (or maj3): major third,
1982:
1742:
1468:
1362:
1198:Fifth from C to G in the A
321:
236:
158:, a unit derived from the
29:
9121:
9073:List of musical intervals
9068:
9032:
8981:
8970:
8892:
8886:Consonance and dissonance
8838:
8796:
8763:
8652:
8622:
8592:
8549:
8540:
8513:
8440:
8423:
8258:to fractional semitones.)
8251:24-tone equal temperament
8248:
8237:
8174:
8119:
8064:
8027:
7990:
7955:
7922:
7843:Gardner, Carl E. (1912):
7469:Bonds, Mark Evan (2006).
7233:; Payne, Dorothy (2008).
7142:Laitz, Steven G. (2016).
7044:Harmony and Voice Leading
6507:
6502:
6497:
6266:
6231:
6196:
6161:
6126:
6091:
6058:
6023:
5988:
5953:
5923:
5890:
5792:
5790:
5769:
5767:
5716:
5706:
5704:
5685:
5681:
5656:
5635:
5628:
5563:
5552:
5531:
5522:
5517:
5512:
5502:
5489:
5463:
5458:
5453:
5441:
5436:
5433:
5428:
4574:
4567:
4564:
4559:
4296:
4271:
4265:
4147:minor major seventh chord
4088:for dominant (the symbol
4084:for half diminished, and
3831:
3829:
3826:
3181:enharmonically equivalent
3097:12-tone equal temperament
2934:
2931:
2926:
2884:enharmonically equivalent
2641:Consonance and dissonance
2636:Consonance and dissonance
2066:
2063:
2058:
1710:As shown in the table, a
1357:§ Compound intervals
1239:one-to-one correspondence
1174:
850:
847:
842:
829:
536:smaller than one semitone
304:12-tone equal temperament
132:enharmonically equivalent
32:Interval (disambiguation)
7831:Longmans, Green, and Co.
7829:(3rd English ed.).
7723:Ockelford, Adam (2005).
7675:(2nd ed.). London:
7358:Helmholtz, Hermann L. F.
7090:"Prime (ii). See Unison"
7016:(2nd ed.). London:
6882:, A–B–C–D–E–F–G) or any
6821:
5546:greater diesis (648:625)
5318:its strongest interval.
4498:Diminished seventh chord
2647:to consonant intervals.
1739:Augmented and diminished
1477:Perfect intervals on C:
1171:) indicates its number.
695:, whole tone, whole step
505:, while that from D to G
317:
162:of the frequency ratio.
8846:List of pitch intervals
8584:Subminor and supermajor
8523:minor diatonic semitone
8433:refer to pitch ratios.)
7858:Encyclopædia Britannica
7817:Helmholtz, H. L. F. von
7444:Hal Leonard Corporation
7211:Weber, Godfrey (1841).
7148:Oxford University Press
7100:(subscription required)
6801:List of pitch intervals
6314:Subminor and supermajor
5451:Other naming convention
4471:Augmented seventh chord
4073:is used for augmented,
3669:Main compound intervals
3316:is half the width of a
2805:or larger being skips.
2797:(sometimes also called
2789:(sometimes also called
2630:Consonant and dissonant
2449:Horizontal, linear, or
2409:download the audio file
2337:download the audio file
215:download the audio file
200:
49:download the audio file
8644:Undecimal quarter tone
7556:The Listening Composer
7272:The Rudiments of Music
6916:Diatonic and chromatic
6729:
6442:ordered pitch interval
6413:Ordered pitch interval
6304:Non-diatonic intervals
6295:heptachordum superflua
6294:
6277:
6259:
6242:
6224:
6207:
6189:
6172:
6154:
6137:
6119:
6102:
6084:
6069:
6051:
6034:
6016:
5999:
5981:
5964:
5934:
5916:
5901:
5883:
5826:
5805:Indian classical music
5390:superparticular number
5374:quarter-comma meantone
5298:
4399:Dominant seventh chord
3655:
3535:
3347:
3158:
3117:quarter-comma meantone
2873:
2728:
2665:common practice period
2656:15th- and 16th-century
2585:
2542:harmonic C-minor scale
2519:
2472:Diatonic and chromatic
2466:Diatonic and chromatic
2314:
1971:The augmented fourth (
1925:
1707:
1525:
1463:non-diatonic intervals
1418:). This is called its
1375:
1207:
1191:
1124:
652:, half tone, half step
540:larger than one octave
443:
8639:Septimal quarter tone
8450:septimal quarter tone
7214:General Music Teacher
6806:Music and mathematics
6718:
6423:twelve-tone technique
6403:Pitch-class intervals
6308:Further information:
6225:hexachordum superflua
5423:for further details.
5293:
5209:meantone temperaments
3910:Diminished fourteenth
3656:
3536:
3336:
3130:
3101:meantone temperaments
2862:
2785:, a step is either a
2717:
2671:Hermann von Helmholtz
2565:
2509:
2312:
1756:
1743:Further information:
1610:
1476:
1370:
1197:
1182:
1114:Main intervals from C
1113:
444:
263:ratios, such as 1:1 (
8826:Incomposite interval
8579:Pythagorean interval
8431:(Numbers in brackets
7939:(Numbers in brackets
7827:Alexander John Ellis
7677:Macmillan Publishers
7579:(Venice, 1558): 162.
7440:Harmony & Theory
7312:. London: Macmillan.
7018:Macmillan Publishers
6894:with a conventional
6513:Number of semitones
6326:septimal minor third
5403:). For instance, in
4272:Component intervals
4158:for further details.
3971:Augmented fourteenth
3551:
3407:
3400:, is determined by:
3368:The diatonic number
3359:compound major third
2849:Enharmonic intervals
2594:chromatic to C major
2424:Melodic and harmonic
379:
8609:Pythagorean apotome
8456:septimal third tone
7490:Aikin, Jim (2004).
7367:Ellis, Alexander J.
6816:Regular temperament
6472:diatonic set theory
5601:chromatic semitone,
5413:four kinds of comma
5109:most often observed
5079:symmetric scale n.1
4446:Major seventh chord
4421:Minor seventh chord
4252:component intervals
4112:For 3-note chords (
4003:Intervals in chords
2710:Simple and compound
2590:diatonic to C major
2540:, occurring in the
1968:) by one semitone.
1749:Diminished interval
71:is a difference in
8722:Septimal semicomma
7575:Gioseffo Zarlino,
7207:perfect consonance
7182:. pp. 16–18.
7150:. pp. 27–31.
7095:Grove Music Online
6730:
6435:musical set theory
6181:Diminished seventh
6155:diapente superflua
5917:unisonus superflua
5837:Pythagorean tuning
5811:Latin nomenclature
5595:or augmented prime
5574:diatonic semitone,
5455:Pythagorean tuning
5405:Pythagorean tuning
5366:Pythagorean tuning
5323:added sixth chords
5299:
5250:asymmetric version
5197:Pythagorean tuning
5157:diminished fourths
4143:interval qualities
3843:Augmented eleventh
3834:Diminished twelfth
3651:
3531:
3348:
3329:Compound intervals
3159:
2874:
2729:
2661:Johannes Tinctoris
2586:
2520:
2496:chromatic interval
2315:
2202:Shorthand notation
1930:chromatic semitone
1926:
1745:Augmented interval
1708:
1568:is between A and D
1526:
1376:
1310:is a second, but F
1275:diatonic numbering
1232:compound intervals
1208:
1192:
1125:
964:Diminished seventh
532:a separate section
439:
253:musical instrument
9242:Intervals (music)
9229:
9228:
9081:
9080:
8852:
8851:
8834:
8833:
8664:Pythagorean comma
8604:Pythagorean limma
8536:
8535:
8532:
8531:
8498:supermajor fourth
8474:supermajor second
8419:
8418:
8233:
8232:
8229:
8228:
7941:are the number of
7759:978-3-540-57394-4
7713:978-0-19-531713-8
7686:978-1-56159-239-5
7516:Introducing Music
7473:, p.123. 2nd ed.
7123:978-0-393-26476-0
7077:978-0-393-33420-3
7027:978-1-56159-239-5
6914:scales (see also
6726:
6708:
6707:
6620:Diminished fifth
6618:Augmented fourth
6499:Specific interval
6480:generic intervals
6462:Specific interval
6417:In post-tonal or
6397:Xenharmonic music
6301:
6300:
6286:Augmented seventh
6251:Diminished octave
6052:ditonus superflua
6008:Diminished fourth
5841:Pythagorean comma
5797:
5796:
5526:Pythagorean comma
5514:diminished second
5409:Pythagorean comma
5384:tuned, and their
5370:five-limit tuning
5294:Intervals in the
5105:equal temperament
5071:
5070:
4834:Augmented fourth
4550:
4549:
3996:
3995:
3890:Augmented twelfth
3650:
3530:
3344:
3194:Pythagorean comma
3187:are approximate.
3155:
3090:diatonic function
3082:
3081:
3022:diminished fourth
2870:
2725:
2689:interval strength
2582:
2538:diminished fourth
2516:
2413:
2341:
2199:
2198:
1447:compound interval
1445:The quality of a
1436:diatonic interval
1432:specific interval
1322:is a third, but G
1121:
1103:
1102:
1078:Augmented seventh
1040:Diminished octave
766:Diminished fourth
604:Diminished second
580:alternative names
521:equal temperament
513:diminished fourth
433:
346:equal temperament
338:logarithmic scale
255:is tuned using a
219:
53:
16:(Redirected from
9249:
9108:
9101:
9094:
9085:
9084:
8976:
8975:
8879:
8872:
8865:
8856:
8855:
8844:
8843:
8734:Septimal kleisma
8547:
8546:
8504:subminor seventh
8486:supermajor third
8438:
8437:
8426:Just intonations
8411:
8410:
8406:
8403:
8391:
8390:
8386:
8383:
8371:
8370:
8366:
8363:
8351:
8350:
8346:
8343:
8331:
8330:
8326:
8323:
8311:
8310:
8306:
8303:
8291:
8290:
8286:
8263:
8262:
8246:
8245:
7953:
7952:
7935:
7934:
7909:
7902:
7895:
7886:
7885:
7876:
7833:
7825:. Translated by
7804:
7803:
7792:10.2307/40285634
7779:Music Perception
7770:
7764:
7763:
7742:
7736:
7721:
7715:
7698:
7692:
7690:
7658:
7652:
7651:
7648:Xenharmonic wiki
7640:
7631:
7617:
7611:
7597:
7586:
7580:
7573:
7567:
7549:
7543:
7533:
7527:
7509:
7503:
7488:
7482:
7467:
7458:
7457:
7428:
7419:
7401:
7390:
7384:
7378:
7355:
7349:
7343:
7337:
7331:
7325:
7319:
7313:
7296:
7290:
7268:
7262:
7244:
7238:
7228:
7222:
7221:
7203:
7194:
7193:
7171:
7162:
7161:
7139:
7128:
7127:
7109:
7103:
7101:
7087:
7081:
7080:
7063:
7057:
7056:
7039:
7033:
7031:
6999:
6990:
6989:
6969:
6954:
6942:
6936:
6928:
6919:
6860:
6841:
6834:
6786:Circle of fifths
6780:
6775:
6774:
6773:
6754:interval hearing
6728:
6727:
6504:Generic interval
6495:
6494:
6466:Generic interval
6431:integer notation
6329:, since it is a
6310:Neutral interval
6297:
6280:
6262:
6245:
6227:
6210:
6192:
6190:semiheptachordum
6175:
6157:
6140:
6122:
6111:Diminished sixth
6105:
6087:
6077:Augmented fourth
6072:
6062:Diminished fifth
6054:
6037:
6019:
6002:
5984:
5973:Augmented second
5967:
5943:Diminished third
5937:
5919:
5909:Augmented unison
5904:
5886:
5846:
5845:
5829:
5742:augmented fourth
5721:diminished fifth
5592:augmented unison
5497:or perfect prime
5473:
5472:
5468:
5426:
5425:
5344:Identity (music)
5276:augmented second
5258:harmonic seventh
5220:
5219:
5215:
5191:
5190:
5186:
5179:
5178:
5174:
5168:
5167:
5163:
5145:diminished sixth
5124:
5123:
5119:
4836:Diminished fifth
4601:
4600:
4596:
4557:
4556:
4505:
4381:
4374:Diminished triad
4263:
4262:
4200:added tone chord
4102:names or symbols
4081:for diminished,
3965:or Double octave
3941:Major fourteenth
3921:Minor fourteenth
3812:Perfect eleventh
3757:Diminished tenth
3737:Augmented octave
3673:
3672:
3660:
3658:
3657:
3652:
3648:
3626:
3625:
3598:
3597:
3582:
3581:
3566:
3565:
3540:
3538:
3537:
3532:
3528:
3515:
3514:
3475:
3474:
3447:
3446:
3422:
3421:
3346:
3345:
3304:septimal kleisma
3297:
3296:
3295:
3293:
3256:
3255:
3157:
3156:
3147:
3146:
3137:
3136:
3123:Minute intervals
3114:
3113:
3108:
3107:
3075:
3074:
3067:
3066:
3055:augmented second
3045:
3044:
3031:
3030:
3013:
3012:
3002:
3001:
2980:
2979:
2969:
2968:
2924:
2923:
2920:
2919:
2914:
2913:
2908:
2907:
2902:
2901:
2872:
2871:
2727:
2726:
2625:
2624:
2619:
2618:
2613:
2612:
2607:
2606:
2601:
2600:
2584:
2583:
2572:
2571:
2535:
2534:
2518:
2517:
2370:
2369:
2364:
2363:
2190:
2189:
2179:
2178:
2155:
2154:
2129:diminished fifth
2118:
2117:
2095:augmented fourth
2056:
2055:
2051:
2050:
2045:
2044:
2036:
2035:
2027:
2026:
2017:
2016:
2011:
2010:
2005:
2004:
1999:
1998:
1967:
1966:
1961:
1960:
1955:
1954:
1949:
1948:
1943:
1942:
1937:
1936:
1924:
1923:
1922:
1920:
1912:
1911:
1910:
1908:
1900:
1899:
1898:
1896:
1888:
1887:
1886:
1884:
1876:
1875:
1874:
1872:
1864:
1863:
1862:
1860:
1852:
1851:
1850:
1848:
1840:
1839:
1838:
1836:
1828:
1827:
1826:
1824:
1816:
1815:
1814:
1812:
1804:
1803:
1802:
1800:
1792:
1791:
1790:
1788:
1780:
1779:
1778:
1776:
1768:
1767:
1766:
1764:
1706:
1705:
1704:
1702:
1694:
1693:
1692:
1690:
1682:
1681:
1680:
1678:
1670:
1669:
1668:
1666:
1658:
1657:
1656:
1654:
1646:
1645:
1644:
1642:
1634:
1633:
1632:
1630:
1622:
1621:
1620:
1618:
1583:
1582:
1573:
1572:
1524:
1523:
1522:
1520:
1512:
1511:
1510:
1508:
1500:
1499:
1498:
1496:
1488:
1487:
1486:
1484:
1420:interval quality
1351:
1350:
1345:
1344:
1339:
1338:
1333:
1332:
1327:
1326:
1321:
1320:
1315:
1314:
1309:
1308:
1299:
1298:
1293:
1292:
1280:If one adds any
1271:diatonic numbers
1268:
1267:
1258:
1257:
1203:
1202:
1147:. For instance,
1141:generic interval
1123:
1122:
1099:
1098:
1097:
1095:
1061:
1060:
1059:
1057:
1023:
1022:
1021:
1019:
985:
984:
983:
981:
947:
946:
945:
943:
909:
908:
907:
905:
888:Diminished sixth
867:Augmented fourth
861:
860:
859:
857:
836:Diminished fifth
825:
824:
823:
821:
787:
786:
785:
783:
749:
748:
747:
745:
728:Augmented second
711:
710:
709:
707:
685:Diminished third
668:
667:
666:
664:
642:Augmented unison
625:
624:
623:
621:
545:
544:
510:
509:
500:
499:
448:
446:
445:
440:
438:
434:
432:
431:
422:
421:
412:
403:
402:
332:. The cent is a
233:Frequency ratios
196:
195:
190:
189:
145:
144:
139:
138:
21:
18:Interval quality
9257:
9256:
9252:
9251:
9250:
9248:
9247:
9246:
9232:
9231:
9230:
9225:
9195:Steps and skips
9117:
9112:
9082:
9077:
9064:
9028:
8977:
8973:
8968:
8888:
8883:
8853:
8848:
8830:
8792:
8759:
8702:Septimal diesis
8648:
8618:
8588:
8542:
8528:
8509:
8432:
8429:
8415:
8408:
8404:
8401:
8399:
8388:
8384:
8381:
8379:
8368:
8364:
8361:
8359:
8348:
8344:
8341:
8339:
8328:
8324:
8321:
8319:
8308:
8304:
8301:
8299:
8288:
8284:
8283:
8273:
8272:
8271:
8267:
8257:
8254:
8241:
8239:
8225:
8170:
8115:
8060:
8023:
7986:
7947:
7942:
7940:
7930:
7928:
7925:
7918:
7913:
7874:
7840:
7812:
7807:
7771:
7767:
7760:
7743:
7739:
7722:
7718:
7699:
7695:
7687:
7659:
7655:
7642:
7641:
7634:
7618:
7614:
7591:
7589:J. F. Niermeyer
7587:
7583:
7574:
7570:
7550:
7546:
7536:Hindemith, Paul
7534:
7530:
7510:
7506:
7489:
7485:
7468:
7461:
7454:
7436:Schroeder, Carl
7429:
7422:
7402:
7393:
7385:
7381:
7356:
7352:
7344:
7340:
7332:
7328:
7320:
7316:
7297:
7293:
7269:
7265:
7247:Prout, Ebenezer
7245:
7241:
7229:
7225:
7219:perfect concord
7204:
7197:
7190:
7172:
7165:
7158:
7140:
7131:
7124:
7110:
7106:
7099:
7088:
7084:
7078:
7064:
7060:
7054:
7040:
7036:
7028:
7000:
6993:
6987:
6973:Prout, Ebenezer
6970:
6966:
6962:
6957:
6944:All triads are
6943:
6939:
6929:
6922:
6874:(such as the C-
6862:The expression
6861:
6844:
6835:
6828:
6824:
6776:
6771:
6769:
6766:
6721:
6713:
6704:Perfect octave
6619:
6614:
6602:Perfect fourth
6532:Perfect unison
6493:
6468:
6460:Main articles:
6458:
6415:
6407:Main articles:
6405:
6336:just intonation
6316:
6306:
6216:Augmented sixth
6146:Augmented fifth
6120:semihexachordum
6043:Augmented third
6017:semidiatessaron
5982:tonus superflua
5867:
5850:
5813:
5602:
5594:
5575:
5570:
5568:
5545:
5529:(524288:531441)
5528:
5524:
5496:
5475:
5470:
5466:
5465:
5437:Specific names
5430:
5386:frequency ratio
5362:
5349:Interval cycles
5346:
5338:Main articles:
5336:
5334:Interval cycles
5327:first inversion
5296:harmonic series
5288:
5246:just intonation
5217:
5213:
5212:
5188:
5184:
5183:
5176:
5172:
5171:
5165:
5161:
5160:
5125:-comma meantone
5121:
5117:
5116:
5101:just intonation
5081:) are shown in
5024:
5017:
4991:
4984:
4960:
4953:
4903:
4895:
4888:
4881:
4863:
4858:
4851:
4842:
4835:
4819:
4811:
4804:
4797:
4776:
4769:
4740:
4735:
4730:
4723:
4697:
4690:
4666:
4659:
4610:
4603:
4598:
4594:
4593:
4587:
4571:
4561:
4555:
4503:
4476:
4379:
4353:Augmented triad
4231:extended chords
4189:interval number
4165:interval and a
4098:
4055:half-diminished
4035:
4015:
4007:Main articles:
4005:
3856:Perfect twelfth
3819:Augmented tenth
3777:Augmented ninth
3696:
3685:
3677:
3671:
3621:
3617:
3593:
3589:
3577:
3573:
3561:
3557:
3552:
3549:
3548:
3510:
3506:
3470:
3466:
3442:
3438:
3417:
3413:
3408:
3405:
3404:
3399:
3392:
3385:
3374:
3339:
3331:
3291:
3288:
3287:
3276:perfect twelfth
3253:
3252:
3169:
3161:Main articles:
3150:
3144:
3143:
3134:
3133:
3125:
3111:
3110:
3105:
3104:
3072:
3071:
3064:
3063:
3042:
3041:
3028:
3027:
3010:
3009:
2999:
2998:
2977:
2976:
2966:
2965:
2936:Staff positions
2928:
2917:
2916:
2911:
2910:
2905:
2904:
2899:
2898:
2865:
2857:
2851:
2779:disjunct motion
2773:(also called a
2767:conjunct motion
2751:
2749:Steps and skips
2745:
2743:Steps and skips
2720:
2712:
2697:Lipps–Meyer law
2693:harmonic series
2638:
2632:
2622:
2621:
2616:
2615:
2610:
2609:
2604:
2603:
2598:
2597:
2577:
2569:
2568:
2532:
2531:
2512:
2500:chromatic scale
2474:
2468:
2436:
2428:Main articles:
2426:
2421:
2420:
2419:
2416:
2415:
2414:
2412:
2394:
2367:
2366:
2361:
2360:
2343:
2342:
2340:
2307:
2301:
2204:
2187:
2186:
2176:
2175:
2165:augmented third
2152:
2151:
2115:
2114:
2068:Staff positions
2060:
2048:
2047:
2042:
2041:
2033:
2032:
2024:
2023:
2014:
2013:
2008:
2007:
2002:
2001:
1996:
1995:
1985:
1964:
1963:
1958:
1957:
1952:
1951:
1946:
1945:
1940:
1939:
1934:
1933:
1918:
1915:
1914:
1906:
1903:
1902:
1894:
1891:
1890:
1882:
1879:
1878:
1870:
1867:
1866:
1858:
1855:
1854:
1846:
1843:
1842:
1834:
1831:
1830:
1822:
1819:
1818:
1810:
1807:
1806:
1798:
1795:
1794:
1786:
1783:
1782:
1774:
1771:
1770:
1762:
1759:
1758:
1751:
1741:
1700:
1697:
1696:
1688:
1685:
1684:
1676:
1673:
1672:
1664:
1661:
1660:
1652:
1649:
1648:
1640:
1637:
1636:
1628:
1625:
1624:
1616:
1613:
1612:
1605:
1603:Major and minor
1580:
1579:
1570:
1569:
1544:) and octaves (
1518:
1515:
1514:
1506:
1503:
1502:
1494:
1491:
1490:
1482:
1479:
1478:
1471:
1365:
1348:
1347:
1342:
1341:
1336:
1335:
1330:
1329:
1324:
1323:
1318:
1317:
1312:
1311:
1306:
1305:
1296:
1295:
1290:
1289:
1265:
1264:
1261:chromatic scale
1255:
1254:
1212:staff positions
1200:
1199:
1188:staff positions
1177:
1116:
1108:
1093:
1090:
1089:
1055:
1052:
1051:
1017:
1014:
1013:
1002:Augmented sixth
979:
976:
975:
941:
938:
937:
926:Augmented fifth
903:
900:
899:
855:
852:
851:
819:
816:
815:
804:Augmented third
781:
778:
777:
743:
740:
739:
705:
702:
701:
662:
659:
658:
619:
616:
615:
578:
568:
557:
549:
507:
506:
497:
496:
458:chromatic scale
454:
427:
423:
417:
413:
411:
407:
398:
394:
380:
377:
376:
372:
365:
326:
320:
257:just intonation
241:
235:
227:
226:
225:
222:
221:
220:
218:
203:
193:
192:
187:
186:
142:
141:
136:
135:
134:notes such as C
61:
60:
59:
56:
55:
54:
52:
35:
28:
23:
22:
15:
12:
11:
5:
9255:
9245:
9244:
9227:
9226:
9224:
9223:
9218:
9213:
9208:
9202:
9197:
9192:
9187:
9182:
9177:
9172:
9167:
9166:
9165:
9155:
9150:
9148:Melodic motion
9145:
9140:
9135:
9130:
9122:
9119:
9118:
9111:
9110:
9103:
9096:
9088:
9079:
9078:
9076:
9075:
9069:
9066:
9065:
9063:
9062:
9057:
9052:
9047:
9042:
9036:
9034:
9030:
9029:
9027:
9026:
9021:
9016:
9011:
9006:
9004:Perfect fourth
9001:
8996:
8991:
8985:
8983:
8979:
8978:
8971:
8969:
8967:
8966:
8961:
8960:
8959:
8954:
8949:
8944:
8942:Changing tones
8939:
8929:
8924:
8919:
8914:
8909:
8904:
8899:
8893:
8890:
8889:
8882:
8881:
8874:
8867:
8859:
8850:
8849:
8839:
8836:
8835:
8832:
8831:
8829:
8828:
8823:
8818:
8813:
8808:
8802:
8800:
8794:
8793:
8791:
8790:
8785:
8780:
8775:
8769:
8767:
8761:
8760:
8758:
8757:
8751:
8745:
8738:
8737:
8731:
8725:
8719:
8713:
8706:
8705:
8699:
8696:Greater diesis
8693:
8686:
8685:
8682:Septimal comma
8679:
8676:Holdrian comma
8673:
8670:Syntonic comma
8667:
8660:
8658:
8650:
8649:
8647:
8646:
8641:
8636:
8630:
8628:
8620:
8619:
8617:
8616:
8611:
8606:
8600:
8598:
8590:
8589:
8587:
8586:
8581:
8576:
8571:
8566:
8561:
8555:
8553:
8544:
8538:
8537:
8534:
8533:
8530:
8529:
8527:
8526:
8519:
8517:
8511:
8510:
8508:
8507:
8501:
8495:
8492:subminor fifth
8489:
8483:
8480:subminor third
8477:
8471:
8465:
8459:
8453:
8446:
8444:
8435:
8421:
8420:
8417:
8416:
8414:
8413:
8393:
8373:
8353:
8333:
8313:
8293:
8276:
8274:
8266:
8260:
8243:
8235:
8234:
8231:
8230:
8227:
8226:
8224:
8223:
8217:
8211:
8205:
8199:
8193:
8187:
8180:
8178:
8172:
8171:
8169:
8168:
8162:
8156:
8150:
8144:
8138:
8132:
8125:
8123:
8117:
8116:
8114:
8113:
8107:
8101:
8095:
8089:
8083:
8077:
8070:
8068:
8062:
8061:
8059:
8058:
8052:
8046:
8040:
8033:
8031:
8025:
8024:
8022:
8021:
8015:
8009:
8003:
7996:
7994:
7988:
7987:
7985:
7984:
7978:
7972:
7966:
7959:
7957:
7950:
7932:
7920:
7919:
7912:
7911:
7904:
7897:
7889:
7883:
7882:
7871:
7866:
7861:
7850:
7839:
7838:External links
7836:
7835:
7834:
7811:
7808:
7806:
7805:
7786:(4): 465–502.
7765:
7758:
7737:
7716:
7693:
7685:
7663:Sadie, Stanley
7653:
7632:
7612:
7581:
7568:
7544:
7528:
7504:
7494:, p. 24.
7483:
7459:
7452:
7446:. p. 77.
7420:
7391:
7387:Helmholtz 1895
7379:
7350:
7348:, p. 182.
7346:Helmholtz 1895
7338:
7334:Helmholtz 1895
7326:
7322:Helmholtz 1895
7314:
7291:
7263:
7239:
7231:Kostka, Stefan
7223:
7205:Definition of
7195:
7188:
7163:
7156:
7129:
7122:
7104:
7082:
7076:
7058:
7053:978-0495189756
7052:
7034:
7026:
7004:Sadie, Stanley
6991:
6986:978-0781207836
6985:
6963:
6961:
6958:
6956:
6955:
6937:
6920:
6912:harmonic minor
6864:diatonic scale
6842:
6825:
6823:
6820:
6819:
6818:
6813:
6808:
6803:
6798:
6793:
6788:
6782:
6781:
6765:
6762:
6758:absolute pitch
6712:
6709:
6706:
6705:
6702:
6699:
6696:
6692:
6691:
6690:Major seventh
6688:
6685:
6682:
6678:
6677:
6676:Minor seventh
6674:
6671:
6668:
6664:
6663:
6660:
6657:
6654:
6650:
6649:
6646:
6643:
6640:
6636:
6635:
6634:Perfect fifth
6632:
6629:
6626:
6622:
6621:
6616:
6611:
6608:
6604:
6603:
6600:
6597:
6594:
6590:
6589:
6586:
6583:
6580:
6576:
6575:
6572:
6569:
6566:
6562:
6561:
6558:
6555:
6552:
6548:
6547:
6544:
6541:
6538:
6534:
6533:
6530:
6527:
6524:
6520:
6519:
6517:Interval class
6514:
6510:
6509:
6508:Diatonic name
6506:
6501:
6492:
6489:
6457:
6454:
6450:interval class
6409:Interval class
6404:
6401:
6393:Adriaan Fokker
6369:neutral second
6321:subminor third
6305:
6302:
6299:
6298:
6291:
6288:
6282:
6281:
6274:
6271:
6270:Perfect octave
6268:
6264:
6263:
6256:
6253:
6247:
6246:
6239:
6236:
6233:
6229:
6228:
6221:
6218:
6212:
6211:
6204:
6201:
6198:
6194:
6193:
6186:
6183:
6177:
6176:
6169:
6166:
6163:
6159:
6158:
6151:
6148:
6142:
6141:
6134:
6131:
6128:
6124:
6123:
6116:
6113:
6107:
6106:
6099:
6096:
6093:
6089:
6088:
6081:
6078:
6074:
6073:
6066:
6063:
6060:
6056:
6055:
6048:
6045:
6039:
6038:
6031:
6028:
6027:Perfect fourth
6025:
6021:
6020:
6013:
6010:
6004:
6003:
5996:
5993:
5990:
5986:
5985:
5978:
5975:
5969:
5968:
5961:
5958:
5955:
5951:
5950:
5948:
5945:
5939:
5938:
5931:
5928:
5925:
5921:
5920:
5913:
5910:
5906:
5905:
5898:
5895:
5892:
5888:
5887:
5880:
5877:
5876:Perfect unison
5874:
5870:
5869:
5864:
5861:
5852:
5823:is from Latin
5812:
5809:
5795:
5794:
5791:
5789:
5786:
5784:perfect octave
5781:
5777:
5776:
5774:
5768:
5766:
5763:
5758:
5754:
5753:
5751:
5749:
5747:
5744:
5738:
5737:
5735:
5733:
5731:
5726:
5723:
5718:
5714:
5713:
5711:
5705:
5703:
5700:
5698:perfect fourth
5695:
5691:
5690:
5684:
5682:
5680:
5677:
5672:
5668:
5667:
5665:
5659:
5657:
5655:
5652:
5647:
5643:
5642:
5640:
5634:
5627:
5624:
5619:
5615:
5614:
5612:
5610:
5604:
5603:minor semitone
5599:
5596:
5588:
5587:
5585:
5583:
5577:
5576:major semitone
5572:
5562:
5559:
5554:
5550:
5549:
5547:
5538:
5537:
5530:
5521:
5519:
5516:
5510:
5509:
5507:
5505:
5503:
5501:
5498:
5494:perfect unison
5491:
5487:
5486:
5483:
5479:
5478:
5462:
5460:5-limit tuning
5457:
5452:
5449:
5439:
5438:
5435:
5432:
5417:syntonic comma
5361:
5358:
5340:Interval cycle
5335:
5332:
5287:
5284:
5239:wolf intervals
5230:5-limit tuning
5075:just intervals
5069:
5068:
5063:
5058:
5053:
5048:
5043:
5042:Perfect octave
5040:
5036:
5035:
5032:
5029:
5026:
5019:
5012:
5009:
5005:
5004:
5001:
4998:
4993:
4986:
4979:
4976:
4972:
4971:
4968:
4965:
4962:
4955:
4948:
4945:
4941:
4940:
4937:
4932:
4929:
4924:
4919:
4916:
4912:
4911:
4908:
4900:
4890:
4883:
4876:
4873:
4869:
4868:
4865:
4860:
4855:
4846:
4837:
4832:
4828:
4827:
4824:
4816:
4806:
4799:
4792:
4791:Perfect fourth
4789:
4785:
4784:
4781:
4771:
4766:
4761:
4756:
4753:
4749:
4748:
4745:
4737:
4732:
4725:
4718:
4715:
4711:
4710:
4707:
4704:
4699:
4692:
4685:
4682:
4678:
4677:
4674:
4671:
4668:
4661:
4654:
4651:
4647:
4646:
4641:
4636:
4631:
4626:
4621:
4620:Perfect unison
4618:
4614:
4613:
4606:
4590:
4583:
4581:5-limit tuning
4577:
4576:
4573:
4572:(pitch ratio)
4569:5-limit tuning
4566:
4563:
4554:
4551:
4548:
4547:
4541:
4535:
4532:
4529:
4523:
4522:
4516:
4510:
4507:
4500:
4494:
4493:
4487:
4481:
4478:
4473:
4467:
4466:
4460:
4457:
4451:
4448:
4442:
4441:
4435:
4432:
4426:
4423:
4417:
4416:
4410:
4407:
4404:
4401:
4395:
4394:
4392:
4386:
4383:
4376:
4370:
4369:
4367:
4361:
4358:
4355:
4349:
4348:
4346:
4343:
4337:
4334:
4328:
4327:
4325:
4322:
4316:
4312:
4311:
4309:
4306:
4303:
4300:
4294:
4293:
4290:
4287:
4284:
4278:
4274:
4273:
4270:
4248:
4247:
4246:
4245:
4234:
4219:
4185:
4178:
4159:
4097:
4094:
4034:
4031:
4004:
4001:
3994:
3993:
3990:
3984:
3982:
3980:
3976:
3975:
3972:
3969:
3966:
3959:
3955:
3954:
3951:
3945:
3942:
3939:
3935:
3934:
3931:
3925:
3922:
3919:
3915:
3914:
3911:
3908:
3905:
3899:
3895:
3894:
3891:
3888:
3885:
3879:
3875:
3874:
3871:
3865:
3862:
3853:
3849:
3848:
3845:
3839:
3838:
3835:
3832:
3830:
3828:
3824:
3823:
3820:
3817:
3814:
3809:
3805:
3804:
3801:
3795:
3792:
3787:
3783:
3782:
3779:
3774:
3771:
3766:
3762:
3761:
3758:
3755:
3752:
3747:
3743:
3742:
3739:
3734:
3731:
3726:
3722:
3721:
3718:
3712:
3710:
3708:
3704:
3703:
3700:
3692:
3689:
3681:
3670:
3667:
3662:
3661:
3647:
3644:
3641:
3638:
3635:
3632:
3629:
3624:
3620:
3616:
3613:
3610:
3607:
3604:
3601:
3596:
3592:
3588:
3585:
3580:
3576:
3572:
3569:
3564:
3560:
3556:
3542:
3541:
3527:
3524:
3521:
3518:
3513:
3509:
3505:
3502:
3499:
3496:
3493:
3490:
3487:
3484:
3481:
3478:
3473:
3469:
3465:
3462:
3459:
3456:
3453:
3450:
3445:
3441:
3437:
3434:
3431:
3428:
3425:
3420:
3416:
3412:
3397:
3390:
3383:
3372:
3352:Main intervals
3330:
3327:
3326:
3325:
3308:
3299:
3258:
3243:
3234:
3220:
3216:septimal comma
3211:
3207:syntonic comma
3202:
3124:
3121:
3086:piano keyboard
3080:
3079:
3076:
3068:
3060:
3057:
3051:
3047:
3046:
3038:
3035:
3032:
3024:
3019:
3015:
3014:
3006:
3003:
2995:
2992:
2989:
2985:
2984:
2981:
2973:
2970:
2962:
2957:
2953:
2952:
2949:
2946:
2943:
2939:
2938:
2933:
2930:
2853:Main article:
2850:
2847:
2827:Melodic motion
2783:diatonic scale
2747:Main article:
2744:
2741:
2739:for details).
2733:Main intervals
2711:
2708:
2704:
2703:
2701:#Interval root
2682:
2668:
2634:Main article:
2631:
2628:
2553:harmonic minor
2504:
2503:
2492:
2489:diatonic scale
2470:Main article:
2467:
2464:
2463:
2462:
2447:
2425:
2422:
2417:
2406:
2403:
2400:
2399:
2398:
2393:
2392:Classification
2390:
2386:interval class
2357:
2356:
2352:
2345:
2344:
2334:
2331:
2303:Main article:
2300:
2297:
2296:
2295:
2292:
2289:
2286:
2283:
2203:
2200:
2197:
2196:
2194:
2191:
2183:
2180:
2172:
2161:
2157:
2156:
2148:
2145:
2142:
2139:
2136:
2126:
2122:
2121:
2119:
2111:
2108:
2105:
2102:
2092:
2088:
2087:
2084:
2081:
2078:
2075:
2071:
2070:
2065:
2062:
2054:
2053:
2038:
2029:
1984:
1981:
1740:
1737:
1712:diatonic scale
1604:
1601:
1538:diatonic scale
1470:
1467:
1373:diatonic scale
1364:
1361:
1247:diatonic scale
1245:(the notes of
1226:) to 8 (e.g.,
1176:
1173:
1107:
1104:
1101:
1100:
1087:
1085:
1083:
1080:
1075:
1072:
1070:Perfect octave
1067:
1063:
1062:
1049:
1047:
1045:
1042:
1037:
1034:
1029:
1025:
1024:
1011:
1009:
1007:
1004:
999:
996:
991:
987:
986:
973:
971:
969:
966:
961:
958:
953:
949:
948:
935:
933:
931:
928:
923:
920:
915:
911:
910:
897:
895:
893:
890:
885:
882:
877:
873:
872:
869:
863:
862:
849:
846:
841:
838:
833:
831:
827:
826:
813:
811:
809:
806:
801:
798:
796:Perfect fourth
793:
789:
788:
775:
773:
771:
768:
763:
760:
755:
751:
750:
737:
735:
733:
730:
725:
722:
717:
713:
712:
699:
696:
690:
687:
682:
679:
674:
670:
669:
656:
653:
647:
644:
639:
636:
631:
627:
626:
613:
611:
609:
606:
601:
598:
596:Perfect unison
593:
589:
588:
585:
582:
575:
572:
564:
561:
553:
462:perfect unison
453:
452:Main intervals
450:
437:
430:
426:
420:
416:
410:
406:
401:
397:
393:
390:
387:
384:
370:
363:
322:Main article:
319:
316:
308:equal-tempered
297:pure intervals
293:just intervals
281:perfect fourth
239:Interval ratio
237:Main article:
234:
231:
223:
212:
209:
206:
205:
204:
202:
199:
128:tuning systems
112:diatonic scale
57:
46:
43:
40:
39:
38:
26:
9:
6:
4:
3:
2:
9254:
9243:
9240:
9239:
9237:
9222:
9221:Voice leading
9219:
9217:
9214:
9212:
9209:
9206:
9203:
9201:
9198:
9196:
9193:
9191:
9188:
9186:
9183:
9181:
9178:
9176:
9173:
9171:
9168:
9164:
9161:
9160:
9159:
9156:
9154:
9151:
9149:
9146:
9144:
9141:
9139:
9136:
9134:
9131:
9129:
9128:
9124:
9123:
9120:
9116:
9109:
9104:
9102:
9097:
9095:
9090:
9089:
9086:
9074:
9071:
9070:
9067:
9061:
9060:Major seventh
9058:
9056:
9055:Minor seventh
9053:
9051:
9048:
9046:
9043:
9041:
9038:
9037:
9035:
9031:
9025:
9022:
9020:
9017:
9015:
9012:
9010:
9009:Perfect fifth
9007:
9005:
9002:
9000:
8997:
8995:
8992:
8990:
8987:
8986:
8984:
8980:
8965:
8962:
8958:
8955:
8953:
8950:
8948:
8945:
8943:
8940:
8938:
8935:
8934:
8933:
8932:Nonchord tone
8930:
8928:
8925:
8923:
8920:
8918:
8915:
8913:
8910:
8908:
8905:
8903:
8900:
8898:
8895:
8894:
8891:
8887:
8880:
8875:
8873:
8868:
8866:
8861:
8860:
8857:
8847:
8837:
8827:
8824:
8822:
8819:
8817:
8814:
8812:
8809:
8807:
8804:
8803:
8801:
8799:
8795:
8789:
8786:
8784:
8781:
8779:
8776:
8774:
8771:
8770:
8768:
8766:
8762:
8755:
8752:
8749:
8746:
8743:
8740:
8739:
8735:
8732:
8729:
8726:
8723:
8720:
8717:
8714:
8711:
8708:
8707:
8703:
8700:
8697:
8694:
8691:
8690:Lesser diesis
8688:
8687:
8683:
8680:
8677:
8674:
8671:
8668:
8665:
8662:
8661:
8659:
8657:
8656:
8651:
8645:
8642:
8640:
8637:
8635:
8632:
8631:
8629:
8627:
8626:
8625:Quarter tones
8621:
8615:
8612:
8610:
8607:
8605:
8602:
8601:
8599:
8597:
8596:
8591:
8585:
8582:
8580:
8577:
8575:
8574:Pseudo-octave
8572:
8570:
8567:
8565:
8562:
8560:
8557:
8556:
8554:
8552:
8548:
8545:
8539:
8524:
8521:
8520:
8518:
8516:
8512:
8505:
8502:
8499:
8496:
8493:
8490:
8487:
8484:
8481:
8478:
8475:
8472:
8469:
8466:
8463:
8460:
8457:
8454:
8451:
8448:
8447:
8445:
8443:
8439:
8436:
8434:
8428:
8427:
8422:
8397:
8394:
8377:
8374:
8357:
8354:
8337:
8334:
8317:
8314:
8297:
8294:
8281:
8278:
8277:
8275:
8270:
8264:
8261:
8259:
8253:
8252:
8247:
8244:
8236:
8221:
8218:
8215:
8212:
8209:
8206:
8203:
8200:
8197:
8194:
8191:
8188:
8185:
8182:
8181:
8179:
8177:
8173:
8166:
8163:
8160:
8157:
8154:
8151:
8148:
8145:
8142:
8139:
8136:
8133:
8130:
8127:
8126:
8124:
8122:
8118:
8111:
8108:
8105:
8102:
8099:
8096:
8093:
8090:
8087:
8084:
8081:
8078:
8075:
8072:
8071:
8069:
8067:
8063:
8056:
8053:
8050:
8047:
8044:
8041:
8038:
8035:
8034:
8032:
8030:
8026:
8019:
8016:
8013:
8010:
8007:
8004:
8001:
7998:
7997:
7995:
7993:
7989:
7982:
7979:
7976:
7973:
7970:
7967:
7964:
7961:
7960:
7958:
7954:
7951:
7949:
7945:
7936:
7933:
7927:
7921:
7917:
7910:
7905:
7903:
7898:
7896:
7891:
7890:
7887:
7881:
7877:
7872:
7870:
7867:
7865:
7862:
7860:
7859:
7854:
7851:
7848:
7847:
7842:
7841:
7832:
7828:
7824:
7823:
7818:
7814:
7813:
7801:
7797:
7793:
7789:
7785:
7781:
7780:
7775:
7769:
7761:
7755:
7751:
7747:
7741:
7734:
7733:0-7546-3573-2
7730:
7727:, p. 7.
7726:
7720:
7714:
7710:
7706:
7702:
7697:
7688:
7682:
7678:
7674:
7673:
7668:
7667:Tyrrell, John
7664:
7657:
7649:
7645:
7639:
7637:
7629:
7625:
7621:
7616:
7609:
7608:90-04-04794-8
7605:
7601:
7595:
7590:
7585:
7578:
7572:
7565:
7564:0-520-06991-9
7561:
7557:
7553:
7552:Perle, George
7548:
7541:
7537:
7532:
7525:
7524:0-14-020659-0
7521:
7517:
7513:
7512:Károlyi, Ottó
7508:
7501:
7500:0-87930-798-6
7497:
7493:
7487:
7480:
7479:0-13-193104-0
7476:
7472:
7466:
7464:
7455:
7453:9780793579914
7449:
7445:
7441:
7437:
7433:
7427:
7425:
7417:
7416:0-02-864737-8
7413:
7409:
7405:
7400:
7398:
7396:
7388:
7383:
7376:
7375:0-486-60753-4
7372:
7368:
7364:
7363:
7359:
7354:
7347:
7342:
7335:
7330:
7323:
7318:
7311:
7307:
7306:Stanley Sadie
7303:
7302:
7295:
7289:
7288:9781873497203
7285:
7281:
7280:9780713507447
7277:
7273:
7267:
7260:
7259:0-403-00326-1
7256:
7252:
7248:
7243:
7236:
7235:Tonal Harmony
7232:
7227:
7220:
7216:
7215:
7208:
7202:
7200:
7191:
7189:9781259447099
7185:
7181:
7177:
7170:
7168:
7159:
7157:9780199347094
7153:
7149:
7145:
7138:
7136:
7134:
7125:
7119:
7115:
7108:
7097:
7096:
7091:
7086:
7079:
7073:
7069:
7062:
7055:
7049:
7045:
7038:
7029:
7023:
7019:
7015:
7014:
7009:
7008:Tyrrell, John
7005:
6998:
6996:
6988:
6982:
6978:
6974:
6968:
6964:
6952:
6947:
6941:
6935:
6927:
6925:
6917:
6913:
6909:
6908:melodic minor
6905:
6904:natural minor
6901:
6897:
6896:key signature
6893:
6889:
6885:
6884:transposition
6881:
6877:
6873:
6872:natural notes
6869:
6865:
6859:
6857:
6855:
6853:
6851:
6849:
6847:
6839:
6833:
6831:
6826:
6817:
6814:
6812:
6811:Pseudo-octave
6809:
6807:
6804:
6802:
6799:
6797:
6794:
6792:
6789:
6787:
6784:
6783:
6779:
6768:
6761:
6759:
6755:
6749:
6747:
6743:
6739:
6735:
6717:
6700:
6697:
6694:
6693:
6686:
6683:
6680:
6679:
6672:
6669:
6666:
6665:
6658:
6655:
6652:
6651:
6644:
6641:
6638:
6637:
6630:
6627:
6624:
6623:
6612:
6609:
6606:
6605:
6598:
6595:
6592:
6591:
6584:
6581:
6578:
6577:
6570:
6567:
6564:
6563:
6560:Major second
6556:
6553:
6550:
6549:
6546:Minor second
6542:
6539:
6536:
6535:
6528:
6525:
6522:
6521:
6518:
6515:
6512:
6511:
6505:
6500:
6496:
6488:
6484:
6481:
6477:
6473:
6467:
6463:
6453:
6451:
6445:
6443:
6438:
6436:
6432:
6428:
6424:
6420:
6414:
6410:
6400:
6398:
6394:
6390:
6386:
6382:
6378:
6374:
6370:
6366:
6362:
6360:
6356:
6351:
6349:
6343:
6341:
6337:
6332:
6328:
6327:
6322:
6315:
6311:
6296:
6292:
6289:
6287:
6284:
6283:
6279:
6275:
6272:
6269:
6265:
6261:
6257:
6254:
6252:
6249:
6248:
6244:
6240:
6237:
6235:Major seventh
6234:
6230:
6226:
6222:
6219:
6217:
6214:
6213:
6209:
6205:
6202:
6200:Minor seventh
6199:
6195:
6191:
6187:
6184:
6182:
6179:
6178:
6174:
6170:
6167:
6164:
6160:
6156:
6152:
6149:
6147:
6144:
6143:
6139:
6135:
6132:
6129:
6125:
6121:
6117:
6114:
6112:
6109:
6108:
6104:
6100:
6097:
6095:Perfect fifth
6094:
6090:
6086:
6082:
6079:
6076:
6075:
6071:
6067:
6064:
6061:
6057:
6053:
6049:
6046:
6044:
6041:
6040:
6036:
6032:
6029:
6026:
6022:
6018:
6014:
6011:
6009:
6006:
6005:
6001:
5997:
5994:
5991:
5987:
5983:
5979:
5976:
5974:
5971:
5970:
5966:
5962:
5959:
5956:
5952:
5949:
5946:
5944:
5941:
5940:
5936:
5932:
5929:
5926:
5922:
5918:
5914:
5911:
5908:
5907:
5903:
5899:
5896:
5893:
5889:
5885:
5881:
5878:
5875:
5872:
5871:
5868:nomenclature
5865:
5862:
5860:
5856:
5853:
5848:
5847:
5844:
5842:
5838:
5832:
5830:
5828:
5822:
5818:
5808:
5806:
5802:
5793:duplex (2:1)
5787:
5785:
5782:
5779:
5778:
5775:
5772:
5771:sesquialterum
5764:
5762:
5761:perfect fifth
5759:
5756:
5755:
5752:
5750:
5748:
5745:
5743:
5740:
5739:
5736:
5734:
5732:
5730:
5724:
5722:
5719:
5715:
5712:
5709:
5708:sesquitertium
5701:
5699:
5696:
5693:
5692:
5688:
5687:sesquiquartum
5683:
5678:
5676:
5673:
5670:
5669:
5666:
5663:
5662:sesquiquintum
5660:
5658:
5653:
5651:
5648:
5645:
5644:
5641:
5638:
5637:sesquioctavum
5632:
5625:
5623:
5620:
5617:
5616:
5613:
5611:
5608:
5605:
5600:
5597:
5593:
5590:
5589:
5586:
5584:
5581:
5578:
5573:
5566:
5560:
5558:
5555:
5551:
5548:
5543:
5540:
5539:
5535:
5527:
5515:
5511:
5508:
5506:
5504:
5499:
5495:
5492:
5488:
5484:
5481:
5480:
5477:
5461:
5456:
5448:
5444:
5440:
5434:Generic names
5427:
5424:
5422:
5418:
5414:
5410:
5406:
5402:
5398:
5395:Typically, a
5393:
5391:
5387:
5383:
5379:
5375:
5371:
5367:
5357:
5354:
5350:
5345:
5341:
5331:
5328:
5324:
5319:
5316:
5312:
5311:interval root
5308:
5304:
5297:
5292:
5286:Interval root
5283:
5281:
5277:
5273:
5271:
5265:
5263:
5259:
5255:
5251:
5247:
5242:
5240:
5236:
5231:
5226:
5224:
5210:
5206:
5202:
5198:
5193:
5181:
5158:
5154:
5150:
5146:
5142:
5138:
5134:
5131:cents, where
5130:
5126:
5112:
5110:
5106:
5102:
5098:
5094:
5090:
5086:
5085:
5080:
5076:
5067:
5062:
5057:
5052:
5047:
5044:
5038:
5037:
5023:
5016:
5013:
5011:Major seventh
5007:
5006:
4997:
4990:
4983:
4980:
4978:Minor seventh
4974:
4973:
4959:
4952:
4949:
4943:
4942:
4936:
4928:
4923:
4920:
4914:
4913:
4906:
4898:
4894:
4887:
4880:
4877:
4875:Perfect fifth
4871:
4870:
4854:
4850:
4845:
4841:
4838:
4830:
4829:
4822:
4814:
4810:
4803:
4796:
4793:
4787:
4786:
4779:
4775:
4765:
4760:
4757:
4751:
4750:
4743:
4729:
4722:
4719:
4713:
4712:
4703:
4696:
4689:
4686:
4680:
4679:
4665:
4658:
4655:
4649:
4648:
4645:
4640:
4635:
4630:
4625:
4622:
4616:
4615:
4612:
4607:
4605:
4591:
4589:
4584:
4582:
4579:
4578:
4570:
4558:
4546:
4542:
4539:
4536:
4533:
4530:
4528:
4525:
4524:
4521:
4517:
4514:
4511:
4508:
4501:
4499:
4496:
4495:
4492:
4488:
4485:
4482:
4479:
4474:
4472:
4469:
4468:
4465:
4461:
4458:
4455:
4452:
4449:
4447:
4444:
4443:
4440:
4436:
4433:
4430:
4427:
4424:
4422:
4419:
4418:
4415:
4411:
4408:
4405:
4402:
4400:
4397:
4396:
4393:
4390:
4387:
4384:
4377:
4375:
4372:
4371:
4368:
4365:
4362:
4359:
4356:
4354:
4351:
4350:
4347:
4344:
4341:
4338:
4335:
4333:
4330:
4329:
4326:
4323:
4320:
4317:
4314:
4313:
4310:
4307:
4304:
4301:
4299:
4295:
4291:
4288:
4285:
4282:
4279:
4276:
4275:
4269:
4264:
4261:
4259:
4258:
4253:
4243:
4239:
4235:
4232:
4228:
4224:
4220:
4217:
4213:
4209:
4205:
4201:
4197:
4196:
4194:
4190:
4186:
4183:
4179:
4176:
4172:
4168:
4167:perfect fifth
4164:
4160:
4157:
4152:
4148:
4144:
4139:
4135:
4131:
4127:
4123:
4119:
4115:
4111:
4110:
4109:
4107:
4103:
4093:
4091:
4087:
4083:
4080:
4076:
4072:
4068:
4064:
4060:
4056:
4052:
4048:
4044:
4040:
4030:
4028:
4024:
4020:
4014:
4010:
4009:Chord (music)
4000:
3991:
3989:
3985:
3983:
3981:
3978:
3977:
3973:
3970:
3967:
3964:
3960:
3957:
3956:
3952:
3950:
3946:
3943:
3940:
3937:
3936:
3932:
3930:
3926:
3923:
3920:
3917:
3916:
3912:
3909:
3906:
3904:
3900:
3897:
3896:
3892:
3889:
3886:
3884:
3880:
3877:
3876:
3872:
3870:
3866:
3863:
3861:
3857:
3854:
3851:
3850:
3846:
3844:
3841:
3840:
3836:
3833:
3825:
3821:
3818:
3815:
3813:
3810:
3807:
3806:
3802:
3800:
3796:
3793:
3791:
3788:
3785:
3784:
3780:
3778:
3775:
3772:
3770:
3767:
3764:
3763:
3759:
3756:
3753:
3751:
3748:
3745:
3744:
3740:
3738:
3735:
3732:
3730:
3727:
3724:
3723:
3719:
3717:
3713:
3711:
3709:
3706:
3705:
3701:
3698:
3693:
3690:
3687:
3684:Minor, major,
3682:
3680:
3675:
3674:
3666:
3645:
3639:
3636:
3633:
3627:
3622:
3618:
3614:
3611:
3608:
3605:
3602:
3599:
3594:
3590:
3586:
3583:
3578:
3574:
3570:
3567:
3562:
3558:
3554:
3547:
3546:
3545:
3525:
3519:
3516:
3511:
3507:
3503:
3497:
3494:
3491:
3488:
3485:
3479:
3476:
3471:
3467:
3463:
3457:
3451:
3448:
3443:
3439:
3435:
3429:
3426:
3423:
3418:
3414:
3410:
3403:
3402:
3401:
3396:
3389:
3382:
3378:
3371:
3366:
3362:
3360:
3355:
3353:
3335:
3323:
3319:
3315:
3314:
3309:
3306:
3305:
3300:
3294:
3285:
3284:perfect fifth
3281:
3277:
3273:
3269:
3265:
3264:
3259:
3250:
3249:
3244:
3241:
3240:
3235:
3232:
3227:
3226:
3221:
3218:
3217:
3212:
3209:
3208:
3203:
3200:
3196:
3195:
3190:
3189:
3188:
3186:
3182:
3178:
3174:
3168:
3164:
3163:Comma (music)
3141:
3138:
3129:
3120:
3118:
3102:
3098:
3093:
3091:
3087:
3077:
3069:
3061:
3058:
3056:
3052:
3049:
3048:
3039:
3036:
3033:
3025:
3023:
3020:
3017:
3016:
3007:
3004:
2996:
2993:
2990:
2987:
2986:
2982:
2974:
2971:
2963:
2961:
2958:
2955:
2954:
2950:
2947:
2944:
2941:
2940:
2937:
2932:Interval name
2925:
2922:
2895:
2893:
2889:
2885:
2881:
2880:
2861:
2856:
2846:
2844:
2840:
2836:
2832:
2828:
2824:
2822:
2818:
2817:tuning system
2813:
2812:) is a skip.
2811:
2806:
2804:
2800:
2796:
2792:
2788:
2784:
2780:
2776:
2772:
2768:
2764:
2760:
2756:
2750:
2740:
2738:
2734:
2716:
2707:
2702:
2698:
2694:
2690:
2686:
2683:
2680:
2676:
2672:
2669:
2666:
2662:
2657:
2653:
2652:
2651:
2648:
2646:
2642:
2637:
2627:
2626:major scale.
2595:
2591:
2574:
2564:
2560:
2558:
2557:melodic minor
2554:
2549:
2547:
2543:
2539:
2528:
2525:
2508:
2501:
2497:
2493:
2490:
2486:
2484:
2479:
2478:
2477:
2473:
2460:
2456:
2452:
2448:
2445:
2441:
2440:
2439:
2435:
2431:
2410:
2397:
2389:
2387:
2382:
2379:
2375:
2372:
2353:
2350:
2349:
2348:
2338:
2328:
2327:
2326:
2324:
2320:
2311:
2306:
2293:
2290:
2287:
2284:
2281:
2280:
2279:
2277:
2273:
2269:
2265:
2261:
2257:
2253:
2249:
2246:is P8, and a
2245:
2241:
2237:
2233:
2229:
2225:
2221:
2217:
2213:
2210:for perfect,
2209:
2195:
2192:
2184:
2181:
2173:
2170:
2166:
2162:
2159:
2158:
2149:
2146:
2143:
2140:
2137:
2134:
2130:
2127:
2124:
2123:
2120:
2112:
2109:
2106:
2103:
2100:
2096:
2093:
2090:
2089:
2085:
2082:
2079:
2076:
2073:
2072:
2069:
2064:Interval name
2057:
2039:
2030:
2021:
2020:
2019:
1992:
1990:
1980:
1978:
1974:
1969:
1931:
1921:
1909:
1897:
1885:
1873:
1861:
1849:
1837:
1825:
1813:
1801:
1789:
1777:
1765:
1755:
1750:
1746:
1736:
1732:
1730:
1726:
1722:
1718:
1713:
1703:
1691:
1679:
1667:
1655:
1643:
1631:
1619:
1609:
1600:
1598:
1594:
1590:
1585:
1577:
1567:
1563:
1559:
1555:
1551:
1547:
1543:
1540:all unisons (
1539:
1534:
1532:
1521:
1509:
1497:
1485:
1475:
1466:
1464:
1461:are used for
1460:
1456:
1452:
1448:
1443:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1405:
1401:
1397:
1393:
1389:
1385:
1381:
1374:
1369:
1360:
1358:
1353:
1301:
1287:
1283:
1278:
1276:
1272:
1262:
1252:
1251:natural minor
1248:
1244:
1240:
1235:
1233:
1229:
1225:
1221:
1217:
1213:
1206:
1196:
1189:
1185:
1181:
1172:
1170:
1166:
1162:
1158:
1154:
1150:
1146:
1142:
1138:
1135:(also called
1134:
1130:
1112:
1096:
1088:
1086:
1084:
1081:
1079:
1076:
1073:
1071:
1068:
1065:
1064:
1058:
1050:
1048:
1046:
1043:
1041:
1038:
1035:
1033:
1032:Major seventh
1030:
1027:
1026:
1020:
1012:
1010:
1008:
1005:
1003:
1000:
997:
995:
994:Minor seventh
992:
989:
988:
982:
974:
972:
970:
967:
965:
962:
959:
957:
954:
951:
950:
944:
936:
934:
932:
929:
927:
924:
921:
919:
916:
913:
912:
906:
898:
896:
894:
891:
889:
886:
883:
881:
880:Perfect fifth
878:
875:
874:
870:
868:
865:
864:
858:
845:
839:
837:
834:
828:
822:
814:
812:
810:
807:
805:
802:
799:
797:
794:
791:
790:
784:
776:
774:
772:
769:
767:
764:
761:
759:
756:
753:
752:
746:
738:
736:
734:
731:
729:
726:
723:
721:
718:
715:
714:
708:
700:
697:
694:
691:
688:
686:
683:
680:
678:
675:
672:
671:
665:
657:
654:
651:
648:
645:
643:
640:
637:
635:
632:
629:
628:
622:
614:
612:
610:
607:
605:
602:
599:
597:
594:
591:
590:
586:
583:
581:
576:
573:
570:
565:
562:
559:
556:Minor, major,
554:
552:
547:
546:
543:
541:
537:
533:
528:
526:
522:
518:
514:
504:
493:
491:
487:
483:
479:
475:
471:
467:
463:
459:
449:
435:
428:
424:
418:
414:
408:
404:
399:
395:
391:
388:
385:
382:
374:
369:
366:to frequency
362:
357:
355:
351:
347:
343:
339:
335:
331:
325:
315:
313:
309:
305:
300:
298:
294:
290:
286:
282:
278:
277:perfect fifth
274:
270:
266:
262:
258:
254:
250:
246:
240:
230:
216:
198:
184:
180:
179:perfect fifth
176:
172:
168:
163:
161:
157:
152:
147:
133:
129:
125:
121:
117:
113:
109:
105:
100:
98:
94:
90:
86:
82:
78:
74:
70:
66:
50:
37:
33:
19:
9137:
9125:
9045:Major second
9040:Minor second
8927:Musical note
8921:
8797:
8764:
8750:(0.72 cents)
8744:(1.95 cents)
8724:(13.8 cents)
8718:(10.1 cents)
8712:(19.5 cents)
8704:(35.7 cents)
8698:(62.6 cents)
8692:(41.1 cents)
8684:(27.3 cents)
8678:(22.6 cents)
8672:(21.5 cents)
8666:(23.5 cents)
8653:
8634:Quarter tone
8624:
8623:
8594:
8593:
8550:
8515:Higher-limit
8430:
8424:
8336:major fourth
8280:quarter tone
8255:
8249:
7938:
7915:
7856:
7849:, p. 38
7845:
7821:
7783:
7777:
7768:
7749:
7740:
7724:
7719:
7704:
7701:Lewin, David
7696:
7670:
7656:
7647:
7619:
7615:
7599:
7584:
7576:
7571:
7555:
7547:
7539:
7531:
7515:
7507:
7491:
7486:
7470:
7439:
7432:Wyatt, Keith
7407:
7382:
7360:
7353:
7341:
7329:
7317:
7310:John Tyrrell
7299:
7294:
7271:
7266:
7250:
7242:
7234:
7226:
7218:
7213:
7206:
7175:
7143:
7113:
7107:
7093:
7085:
7067:
7061:
7043:
7037:
7011:
6976:
6967:
6951:minor thirds
6940:
6932:
6868:7-tone scale
6791:Ear training
6778:Music portal
6750:
6737:
6731:
6662:Major sixth
6648:Minor sixth
6588:Major third
6574:Minor third
6485:
6469:
6446:
6439:
6416:
6388:
6384:
6380:
6376:
6373:Arabic music
6365:quarter tone
6358:
6354:
6347:
6344:
6324:
6320:
6317:
6260:semidiapason
5927:Major second
5894:Minor second
5833:
5824:
5814:
5798:
5633:, whole step
5622:major second
5557:minor second
5394:
5377:
5363:
5353:George Perle
5347:
5320:
5314:
5310:
5300:
5268:
5266:
5243:
5227:
5211:, including
5204:
5200:
5194:
5152:
5148:
5136:
5132:
5128:
5113:
5096:
5082:
5072:
5065:
5060:
5055:
5050:
5045:
5021:
5014:
4995:
4988:
4981:
4957:
4950:
4934:
4926:
4921:
4892:
4885:
4878:
4852:
4848:
4843:
4839:
4808:
4801:
4794:
4773:
4763:
4758:
4727:
4720:
4701:
4694:
4687:
4684:Major second
4663:
4656:
4653:Minor second
4643:
4638:
4633:
4628:
4623:
4544:
4537:
4531:C, Cm, or Cm
4519:
4512:
4490:
4483:
4463:
4453:
4438:
4428:
4413:
4388:
4363:
4339:
4318:
4255:
4251:
4249:
4156:main article
4101:
4099:
4089:
4085:
4082:
4078:
4074:
4070:
4066:
4036:
4016:
3997:
3695:Augmented or
3663:
3543:
3394:
3387:
3380:
3376:
3369:
3367:
3363:
3358:
3356:
3349:
3313:quarter tone
3311:
3302:
3275:
3271:
3268:minor thirds
3261:
3246:
3237:
3233:for details.
3223:
3214:
3205:
3192:
3170:
3094:
3083:
2929:of semitones
2896:
2883:
2877:
2875:
2842:
2838:
2834:
2830:
2825:
2814:
2807:
2798:
2795:major second
2790:
2787:minor second
2778:
2774:
2770:
2766:
2762:
2758:
2754:
2752:
2730:
2705:
2695:. See also:
2688:
2679:fundamentals
2649:
2644:
2639:
2593:
2589:
2587:
2550:
2546:main article
2529:
2521:
2495:
2481:
2476:In general,
2475:
2458:
2454:
2442:Vertical or
2437:
2395:
2383:
2380:
2376:
2373:
2358:
2346:
2316:
2278:. Examples:
2275:
2271:
2267:
2263:
2259:
2255:
2235:
2227:
2219:
2211:
2207:
2205:
2168:
2132:
2098:
2061:of semitones
1993:
1986:
1976:
1972:
1970:
1927:
1733:
1728:
1724:
1720:
1716:
1709:
1586:
1578:is between D
1575:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1535:
1531:contrapuntal
1527:
1458:
1454:
1450:
1444:
1439:
1435:
1431:
1423:
1419:
1415:
1407:
1399:
1391:
1383:
1379:
1377:
1354:
1302:
1279:
1274:
1270:
1236:
1227:
1223:
1215:
1209:
1168:
1164:
1160:
1156:
1152:
1148:
1144:
1140:
1136:
1132:
1129:music theory
1126:
677:Major second
634:Minor second
567:Augmented or
534:. Intervals
529:
494:
478:major second
455:
375:
367:
360:
358:
327:
324:Cent (music)
301:
296:
292:
242:
228:
164:
148:
101:
92:
88:
84:
80:
76:
68:
65:music theory
62:
36:
9033:Dissonances
9019:Major sixth
9014:Minor sixth
8999:Major third
8994:Minor third
8982:Consonances
8952:Preparation
8947:Pedal point
8783:Millioctave
8765:Measurement
8756:(0.4 cents)
8736:(7.7 cents)
8730:(8.1 cents)
8614:Major limma
8356:minor fifth
7592: [
7404:Cope, David
7180:McGraw Hill
6888:accidentals
6880:minor scale
6876:major scale
6742:time points
6734:David Lewin
6165:Major sixth
6130:Minor sixth
6035:diatessaron
5992:Major third
5965:semiditonus
5957:Minor third
5675:major third
5650:minor third
5609:(2187:2048)
5544:(2048:2025)
5280:minor third
5272:equivalents
5155:, actually
4947:Major sixth
4918:Minor sixth
4755:Major third
4717:Minor third
4611:temperament
4586:Pythagorean
4450:CM, or Cmaj
4425:Cm, or Cmin
4357:C+, or Caug
4336:Cm, or Cmin
4332:Minor triad
4315:CM, or Cmaj
4298:Major triad
4242:power chord
4208:perfect 4th
4171:major triad
4163:major third
4023:major triad
3947:Diminished
3867:Diminished
3797:Diminished
3790:Major tenth
3769:Minor tenth
3750:Major ninth
3729:Minor ninth
3714:Diminished
2991:major third
2960:major third
2821:pitch space
2810:major third
2803:minor third
1593:pitch class
1282:accidentals
1237:There is a
1205:major scale
1149:major third
1127:In Western
956:Major sixth
918:Minor sixth
758:Major third
720:Minor third
577:Widely used
503:major third
490:major third
334:logarithmic
289:minor third
285:major third
273:major sixth
249:frequencies
175:minor third
8957:Resolution
8902:Avoid note
8816:Semiditone
8710:Diaschisma
8525:(17-limit)
8216:(22 or 23)
8214:fourteenth
8210:(20 or 21)
8208:thirteenth
8204:(18 or 19)
8198:(17 or 18)
8192:(15 or 16)
8186:(13 or 14)
8121:Diminished
7948:interval.)
7929:(post-Bach
7853:"Interval"
7628:0803279345
6960:References
6491:Comparison
6359:supermajor
6340:microtonal
5631:whole tone
5569:half tone,
5542:diaschisma
5536:(128:125)
5523:descending
5303:David Cope
5274:, such as
5270:enharmonic
5141:wolf fifth
4562:semitones
4193:chord root
4182:diminished
4169:interval (
4134:diminished
4051:diminished
3986:Augmented
3929:thirteenth
3927:Augmented
3903:thirteenth
3883:thirteenth
3869:thirteenth
3697:diminished
3686:or perfect
3322:whole tone
3239:diaschisma
3173:microtones
2879:enharmonic
2855:Enharmonic
2799:whole step
2685:David Cope
2522:The table
2459:descending
2232:diminished
1574:, and the
1459:supermajor
1412:diminished
569:diminished
558:or perfect
517:instrument
474:whole tone
130:, between
120:microtones
77:horizontal
9211:Ululation
8778:Centitone
8716:Semicomma
8595:Semitones
8559:Microtone
8543:intervals
8220:fifteenth
8066:Augmented
7944:semitones
7916:Intervals
7819:(1895) .
6836:The term
6760:hearing.
6427:serialism
6361:intervals
5902:semitonus
5851:semitones
5849:Number of
5827:semitonus
5582:(256:243)
5571:half step
5431:semitones
5429:Number of
5307:Hindemith
5093:non-equal
4560:Number of
4506:, or Cdim
4475:C+, Caug,
4382:, or Cdim
4283:examples
4212:major 6th
4204:major 2nd
4175:minor 7th
4130:augmented
4126:root note
4047:augmented
3988:fifteenth
3963:fifteenth
3949:fifteenth
3699:intervals
3688:intervals
3679:semitones
3676:Number of
3637:−
3628:−
3517:−
3477:−
3449:−
3199:frequency
3167:Microtone
2892:semitones
2791:half step
2781:. In the
2455:ascending
2384:Since an
2299:Inversion
2240:augmented
2000:, C and G
1989:semitones
1597:harmonics
1589:inversion
1536:Within a
1428:chromatic
1404:augmented
1190:indicated
571:intervals
560:intervals
551:semitones
548:Number of
480:), and a
405:
392:⋅
350:semitones
251:. When a
247:of their
160:logarithm
9236:Category
9207:(figure)
9190:Sequence
9175:Phrasing
9158:Ornament
9138:Interval
9127:Balungan
8937:Cambiata
8922:Interval
8897:Argument
8748:Breedsma
8196:eleventh
8176:Compound
7931:Western)
7926:semitone
7800:40285634
7748:(1993).
7703:(1987).
7669:(eds.).
7554:(1990).
7538:(1934).
7514:(1965),
7438:(1998).
7406:(1997).
7249:(1903).
7010:(eds.).
6910:and the
6902:and the
6764:See also
6476:specific
6355:subminor
6350:interval
6342:scales.
6278:diapason
6103:diapente
6085:tritonus
5884:unisonus
5821:semitone
5565:semitone
5476:meantone
4604:meantone
4292:Seventh
4257:boldface
4223:dominant
4128:, while
4059:dominant
3961:Perfect
3799:eleventh
3354:below).
3318:semitone
3270:and one
3254:♭
3145:♮
3135:♯
3112:♭
3106:♯
3073:♯
3065:♭
3043:♭
3029:♯
3011:♭
3000:♭
2978:♯
2967:♯
2918:♭
2912:♯
2906:♭
2900:♯
2843:disjunct
2839:skipwise
2835:conjunct
2831:stepwise
2819:and the
2645:resolved
2623:♭
2617:♭
2611:♭
2605:♭
2599:♭
2570:♭
2533:♭
2485:interval
2483:diatonic
2444:harmonic
2368:♭
2362:♭
2319:inverted
2188:♯
2177:♭
2153:♭
2116:♯
2049:♯
2043:♭
2034:♭
2025:♯
2015:♯
2009:♭
2003:♭
1997:♯
1965:♯
1959:♯
1953:♯
1947:♭
1941:♯
1935:♭
1581:♯
1571:♯
1455:subminor
1440:interval
1424:modifier
1363:Quality
1349:♯
1343:♯
1337:♯
1331:♯
1325:♯
1319:♯
1313:♯
1307:♯
1297:♭
1291:♯
1266:♯
1256:♯
1201:♭
650:Semitone
508:♭
498:♯
470:semitone
354:semitone
287:), 6:5 (
283:), 5:4 (
279:), 4:3 (
275:), 3:2 (
271:), 5:3 (
267:), 2:1 (
194:♭
188:♯
143:♭
137:♯
116:semitone
93:harmonic
89:vertical
69:interval
9170:Pattern
9143:Melisma
9133:Cadence
9050:Tritone
8964:Spectra
8912:Cadence
8907:Beating
8754:Ragisma
8742:Schisma
8728:Kleisma
8564:5-limit
8470:(15:14)
8464:(21:20)
8458:(28:27)
8452:(36:35)
8442:7-limit
8407:⁄
8396:seventh
8387:⁄
8367:⁄
8347:⁄
8327:⁄
8307:⁄
8287:⁄
8269:Neutral
8242:systems
8202:twelfth
8159:seventh
8110:seventh
8055:seventh
8018:seventh
7956:Perfect
7924:Twelve-
7880:YouTube
7810:Sources
7282:(pbk).
6946:tertian
6838:tritone
6746:timbres
6348:neutral
6331:7-limit
6000:ditonus
5855:Quality
5801:shrutis
5729:tritone
5607:apotome
5532:lesser
5469:⁄
5443:Quality
5378:sesqui-
5254:tritone
5216:⁄
5187:⁄
5175:⁄
5164:⁄
5120:⁄
5089:rounded
4597:⁄
4477:C, or C
4403:C, or C
4240:) is a
4227:seventh
4063:symbols
3860:Tritave
3393:, ...,
3282:plus a
3272:tritave
3263:kleisma
3248:schisma
3078:
3053:doubly
2983:
2888:pitches
2451:melodic
2430:Harmony
2252:tritone
2163:doubly
2006:, and C
1983:Example
1584:and A.
1469:Perfect
1451:neutral
1410:), and
1380:perfect
1359:below.
1346:, and F
1286:natural
1243:degrees
1186:, with
1145:quality
844:Tritone
482:tritone
261:integer
191:and G–A
183:spelled
167:quality
104:Western
85:melodic
9200:Timbre
9185:Rhythm
9115:Melody
9024:Octave
8989:Unison
8811:Ditone
8798:Others
8788:Savart
8655:Commas
8551:Groups
8500:(10:7)
8296:second
8240:tuning
8165:octave
8141:fourth
8129:second
8092:fourth
8080:second
8074:unison
8037:second
8000:second
7981:octave
7969:fourth
7963:unison
7946:in the
7798:
7756:
7731:
7711:
7683:
7626:
7606:
7562:
7522:
7498:
7477:
7450:
7414:
7373:
7286:
7278:
7257:
7186:
7154:
7120:
7074:
7050:
7024:
6983:
6419:atonal
5859:number
5689:(5:4)
5629:tone,
5534:diesis
5485:Short
5474:-comma
5447:number
5382:justly
5139:, the
5111:one).
4905:(wolf)
4897:(wolf)
4821:(wolf)
4813:(wolf)
4778:(wolf)
4742:(wolf)
4602:-comma
4588:tuning
4504:°
4380:°
4289:Fifth
4286:Third
4281:Symbol
4268:chords
4151:number
4114:triads
4061:. The
4057:, and
3901:Major
3881:Minor
3702:Short
3649:
3529:
3280:octave
3257:in C.)
3231:diesis
3225:diesis
3177:commas
3059:
3037:
3034:
3005:
2994:
2972:
2927:Number
2823:used.
2777:), or
2573:-major
2434:Melody
2355:versa.
2323:octave
2248:unison
2244:octave
2193:
2182:
2147:
2144:
2141:
2110:
2107:
2059:Number
2018:, but
1457:, and
1175:Number
1143:) and
1133:number
587:Audio
486:ditone
342:octave
269:octave
265:unison
171:number
124:commas
81:linear
9216:Voice
9180:Pitch
9163:Trill
9153:Motif
8917:Chord
8821:Secor
8569:Comma
8541:Other
8506:(7:4)
8494:(7:5)
8488:(9:7)
8482:(7:6)
8476:(8:7)
8376:sixth
8316:third
8238:Other
8190:tenth
8184:ninth
8153:sixth
8147:fifth
8135:third
8104:sixth
8098:fifth
8086:third
8049:sixth
8043:third
8029:Minor
8012:sixth
8006:third
7992:Major
7975:fifth
7796:JSTOR
7596:]
7209:from
6900:major
6892:staff
6890:on a
6822:Notes
6756:over
6385:super
5935:tonus
5866:Latin
5863:Short
5817:Latin
5773:(3:2)
5710:(4:3)
5664:(6:5)
5639:(9:8)
5580:limma
5397:comma
5103:. In
5034:1100
5018:50:27
5003:1000
4954:27:16
4882:40:27
4844:25:18
4840:45:32
4798:27:20
4724:32:27
4660:27:25
4657:16:15
4609:Equal
4565:Name
4277:Name
4266:Main
4214:(see
4210:, or
4138:fifth
4122:minor
4118:major
4043:minor
4039:major
3716:ninth
3691:Short
3185:cents
3109:and G
2915:and B
2903:and G
2882:, or
2793:) or
2765:, or
2759:skips
2755:steps
2737:below
2675:beats
2614:and E
2575:scale
2524:above
2224:major
2216:minor
2012:and E
1396:minor
1388:major
1220:table
1184:Staff
1165:third
1157:major
584:Short
574:Short
563:Short
525:cents
511:is a
501:is a
466:cents
330:cents
318:Cents
295:, or
245:ratio
156:cents
151:ratio
140:and D
110:of a
108:notes
97:chord
83:, or
73:pitch
67:, an
9205:Type
8806:Wolf
8773:Cent
8222:(24)
8167:(11)
8112:(12)
8106:(10)
8057:(10)
8020:(11)
7983:(12)
7754:ISBN
7729:ISBN
7709:ISBN
7681:ISBN
7624:ISBN
7604:ISBN
7560:ISBN
7520:ISBN
7496:ISBN
7475:ISBN
7448:ISBN
7412:ISBN
7371:ISBN
7308:and
7284:ISBN
7276:ISBN
7255:ISBN
7184:ISBN
7152:ISBN
7118:ISBN
7072:ISBN
7048:ISBN
7022:ISBN
6981:ISBN
6478:and
6464:and
6411:and
6383:and
6357:and
6338:and
6312:and
5857:and
5482:Full
5445:and
5380:are
5342:and
5305:and
5278:for
5228:The
5195:The
5097:each
5084:bold
5066:1200
5061:1200
5056:1200
5051:1200
5031:1083
5028:1110
5025:1067
5022:1088
5015:15:8
5000:1007
4992:1018
4982:16:9
4970:900
4939:800
4910:700
4867:600
4826:500
4783:400
4747:300
4709:200
4691:10:9
4676:100
4238:dyad
4229:and
4132:and
4027:dyad
4019:root
4011:and
3992:A15
3974:A14
3953:d15
3933:A13
3913:d14
3893:A12
3873:d13
3847:A11
3837:d12
3822:A10
3803:d11
3760:d10
3292:Play
3278:(an
3165:and
2775:leap
2771:skip
2763:step
2761:. A
2699:and
2555:and
2432:and
2260:perf
2238:for
2230:for
2222:for
2214:for
1747:and
1587:The
1552:and
1422:(or
1151:(or
1094:Play
1056:Play
1018:Play
980:Play
942:Play
904:Play
856:Play
820:Play
782:Play
744:Play
706:Play
693:Tone
663:Play
620:Play
468:. A
460:. A
389:1200
201:Size
8161:(9)
8155:(7)
8149:(6)
8143:(4)
8137:(2)
8131:(0)
8100:(8)
8094:(6)
8088:(5)
8082:(3)
8076:(1)
8051:(8)
8045:(3)
8039:(1)
8014:(9)
8008:(4)
8002:(2)
7977:(7)
7971:(5)
7965:(0)
7878:on
7788:doi
6736:'s
6470:In
6425:or
6381:sub
5315:top
5241:).
5143:or
5114:In
5046:2:1
4996:996
4989:996
4985:9:5
4967:890
4964:906
4961:906
4958:884
4951:5:3
4935:814
4931:792
4927:814
4922:8:5
4907:738
4902:697
4899:678
4893:702
4889:680
4886:702
4879:3:2
4864:621
4862:579
4859:588
4857:612
4853:569
4849:590
4823:462
4818:503
4815:522
4809:498
4805:520
4802:498
4795:4:3
4780:427
4774:386
4770:384
4768:408
4764:386
4759:5:4
4744:269
4739:310
4736:318
4734:294
4731:294
4728:316
4721:6:5
4706:193
4702:204
4698:182
4695:204
4688:9:8
4673:117
4667:133
4664:112
4624:1:1
4120:or
4116:),
4086:dom
4079:dim
4077:or
4071:aug
4069:or
3968:P15
3944:M14
3924:m14
3907:M13
3887:m13
3864:P12
3858:or
3816:P11
3794:M10
3781:A9
3773:m10
3741:A8
3720:d9
3274:or
3140:+++
2841:or
2833:or
2757:or
2654:In
2536:(a
2276:aug
2272:dim
2268:maj
2264:min
2169:AA3
2031:C–G
2022:C–F
1731:).
1402:),
1394:),
1386:),
1139:or
871:A4
396:log
373:is
177:or
102:In
91:or
63:In
9238::
8400:10
7855:,
7794:.
7784:11
7782:.
7679:.
7665:;
7646:.
7635:^
7598:,
7594:de
7462:^
7442:.
7434:;
7423:^
7394:^
7217:.
7198:^
7166:^
7132:^
7092:,
7020:.
7006:;
6994:^
6923:^
6918:).
6845:^
6829:^
6744:,
6695:12
6681:11
6667:10
6613:3
6474:,
6452:.
6429:,
6399:.
6290:A7
6273:P8
6267:12
6255:d8
6238:M7
6232:11
6220:A6
6203:m7
6197:10
6185:d7
6168:M6
6150:A5
6133:m6
6115:d6
6098:P5
6080:A4
6065:d5
6047:A3
6030:P4
6012:d4
5995:M3
5977:A2
5960:m3
5947:d3
5930:M2
5912:A1
5897:m2
5879:P1
5831:.
5807:.
5788:P8
5780:12
5765:P5
5746:A4
5725:d5
5702:P4
5679:M3
5654:m3
5626:M2
5598:A1
5561:m2
5518:d2
5500:P1
5368:,
5282:.
5264:.
5225:.
5182:.
5039:12
5008:11
4975:10
4670:90
4534:m3
4509:m3
4480:M3
4459:P5
4434:P5
4409:P5
4406:M3
4385:m3
4360:M3
4345:P5
4324:P5
4308:P5
4305:M3
4233:).
4218:).
4206:,
4108:.
4053:,
4049:,
4045:,
4041:,
3979:25
3958:24
3938:23
3918:22
3898:21
3878:20
3852:19
3827:18
3808:17
3786:16
3765:15
3754:M9
3746:14
3733:m9
3725:13
3707:12
3395:DN
3388:DN
3386:,
3381:DN
3370:DN
3310:A
3301:A
3298:).
3260:A
3245:A
3236:A
3222:A
3213:A
3204:A
3191:A
3148:).
2951:4
2894:.
2602:–E
2548:.
2494:A
2480:A
2274:,
2270:,
2266:,
2262:,
2256:TT
2234:,
2226:,
2218:,
2133:d5
2099:A4
2086:5
2046:–E
1977:d5
1973:A4
1962:–C
1938:–C
1919:A8
1913:,
1907:d8
1901:,
1895:A7
1889:,
1883:d7
1877:,
1871:A6
1865:,
1859:d6
1853:,
1847:A5
1841:,
1835:d5
1829:,
1823:A4
1817:,
1811:d4
1805:,
1799:A3
1793:,
1787:d3
1781:,
1775:A2
1769:,
1763:d2
1729:m3
1725:M3
1721:d5
1717:P5
1701:M7
1695:,
1689:m7
1683:,
1677:M6
1671:,
1665:m6
1659:,
1653:M3
1647:,
1641:m3
1635:,
1629:M2
1623:,
1617:m2
1576:d5
1566:A4
1562:d5
1558:A4
1554:P5
1550:P4
1546:P8
1542:P1
1519:P8
1513:,
1507:P5
1501:,
1495:P4
1489:,
1483:PU
1465:.
1453:,
1442:.
1434:,
1277:.
1234:.
1228:d8
1224:P1
1216:m3
1153:M3
1082:A7
1074:P8
1066:12
1044:d8
1036:M7
1028:11
1006:A6
998:m7
990:10
968:d7
960:M6
930:A5
922:m6
892:d6
884:P5
848:TT
840:d5
808:A3
800:P4
770:d4
762:M3
732:A2
724:m3
689:d3
681:M2
646:A1
638:m2
608:d2
600:P1
356:.
314:.
299:.
197:.
99:.
79:,
9107:e
9100:t
9093:v
8878:e
8871:t
8864:v
8412:)
8409:2
8405:1
8402:+
8398:(
8392:)
8389:2
8385:1
8382:+
8380:8
8378:(
8372:)
8369:2
8365:1
8362:+
8360:6
8358:(
8352:)
8349:2
8345:1
8342:+
8340:5
8338:(
8332:)
8329:2
8325:1
8322:+
8320:3
8318:(
8312:)
8309:2
8305:1
8302:+
8300:1
8298:(
8292:)
8289:2
8285:1
8282:(
7908:e
7901:t
7894:v
7802:.
7790::
7762:.
7691:
7689:.
7650:.
7630:.
7610:.
7566:.
7526:.
7502:.
7481:.
7456:.
7418:.
7261:.
7192:.
7160:.
7126:.
7102:)
7032:
7030:.
6701:7
6698:0
6687:6
6684:1
6673:6
6670:2
6659:5
6656:3
6653:9
6645:5
6642:4
6639:8
6631:4
6628:5
6625:7
6615:4
6610:6
6607:6
6599:3
6596:5
6593:5
6585:2
6582:4
6579:4
6571:2
6568:3
6565:3
6557:1
6554:2
6551:2
6543:1
6540:1
6537:1
6529:0
6526:0
6523:0
6162:9
6127:8
6092:7
6059:6
6024:5
5989:4
5954:3
5924:2
5891:1
5873:0
5757:7
5717:6
5694:5
5671:4
5646:3
5618:2
5567:,
5553:1
5490:0
5471:4
5467:1
5218:4
5214:1
5205:ε
5203:(
5201:ε
5189:4
5185:1
5177:4
5173:1
5166:4
5162:1
5153:ε
5149:ε
5137:ε
5133:ε
5129:ε
5122:4
5118:1
4944:9
4915:8
4872:7
4831:6
4788:5
4752:4
4714:3
4681:2
4650:1
4644:0
4639:0
4634:0
4629:0
4617:0
4599:4
4595:1
4545:7
4543:m
4540:5
4538:d
4520:7
4518:d
4515:5
4513:d
4502:C
4491:7
4489:m
4486:5
4484:A
4464:7
4462:M
4456:3
4454:M
4439:7
4437:m
4431:3
4429:m
4414:7
4412:m
4391:5
4389:d
4378:C
4366:5
4364:A
4342:3
4340:m
4321:3
4319:M
4302:C
4090:−
4075:°
4067:+
3646:,
3643:)
3640:1
3634:n
3631:(
3623:n
3619:N
3615:D
3612:+
3609:.
3606:.
3603:.
3600:+
3595:2
3591:N
3587:D
3584:+
3579:1
3575:N
3571:D
3568:=
3563:c
3559:N
3555:D
3526:,
3523:)
3520:1
3512:n
3508:N
3504:D
3501:(
3498:+
3495:.
3492:.
3489:.
3486:+
3483:)
3480:1
3472:2
3468:N
3464:D
3461:(
3458:+
3455:)
3452:1
3444:1
3440:N
3436:D
3433:(
3430:+
3427:1
3424:=
3419:c
3415:N
3411:D
3398:n
3391:2
3384:1
3377:n
3373:c
3070:A
3062:G
3050:4
3040:B
3026:F
3018:4
3008:B
2997:G
2988:4
2975:A
2964:F
2956:4
2948:3
2945:2
2942:1
2567:A
2502:.
2491:.
2461:.
2411:.
2339:.
2236:A
2228:d
2220:M
2212:m
2208:P
2185:E
2174:C
2171:)
2167:(
2160:6
2150:G
2138:C
2135:)
2131:(
2125:6
2113:F
2104:C
2101:)
2097:(
2091:6
2083:4
2080:3
2077:2
2074:1
2040:C
1416:d
1414:(
1408:A
1406:(
1400:m
1398:(
1392:M
1390:(
1384:P
1382:(
1169:3
1167:(
1161:M
1159:(
952:9
914:8
876:7
830:6
792:5
754:4
716:3
698:T
673:2
655:S
630:1
592:0
436:)
429:1
425:f
419:2
415:f
409:(
400:2
386:=
383:n
371:2
368:f
364:1
361:f
217:.
51:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.